







4 games in 4 time slots with 8 teams 
20151016 

From Paul: I'm trying to set up a game matrix for my kids that will have 4 games in 4 time slots with 8 teams. And every team is playing a different game in a different time slot. I provided the initial matrix and I am trying to ensure that no 2 teams play each other more than once. That's my problem.
8 pm 9 pm 10 pm 11 pm
Crokinole 1 vs 2
Trivial Pursuit 3 vs 4
Darts 5 vs 6
Pictionary 7 vs 8
Please help, I've been at it for hours. Answered by Robert Dawson and Victoria West. 





Matrices 
20131110 

From Ricky: Why must we have brackets around matrices. Why don't we just neatly write an array of entries crosswise and up and down to indicate a particular matrix? Answered by Chris Fisher. 





Row echelon form 
20130315 

From Shawn: Please help me put matrix in row echelon form:
1 9 8 0
5 8 1 35
1 4 1 17 Answered by Penny Nom. 





The (i, j) entry of a matrix 
20120217 

From Bilyaminu: Question Bilyaminu
Find a formula for the (i,j) entry of a matrices: A= [1 2 3 4; 5 6 7 8; 9 10 11 12; 13 14 15 16] Answered by Harley Weston. 





Augmented matrix 
20111214 

From Britney: Write Augmented matrix and use row reduction to solve.
I need major help with this problem! Tomorrow is my semester test and I have no idea how to do this.
2x+5y=8
yx=10 Answered by Robert Dawson. 





Geocaching 
20101015 

From Clint: I am stuck on a puzzle for Geocaching which is a GPS game.
I know it is a number matrix but don't know how to start.
[1 7 16 3 9; 1 3 18 20 33] x [1 8 9 3 5; 0 1 0 4 2; 0 0 1 2 1; 0 0 0 1 1; 0 0 0 0 1] = ? Answered by Stephen La Rocque. 





Reflection in the line y = x 
20100721 

From tousif: Find the 2 x 2 matrix which represents a reflection in the line y = x?
Please help.... Answered by Penny Nom. 





The adjacency matrix of an undirected graph 
20100115 

From Bhavya: Let Cn be the undirected graph with vertex set V = {1,2,3,...,n} and edge set E = {(1,2), (2,3), (3,4),.... , (n1,n), (n,1)}. Let An be the adjacency matrix of Cn.
a. Find the determinant of An.
b. Find (An)^2 Answered by Robert Dawson. 





Elements of a Matrix 
20091228 

From peter: I have a array of 10 by 6 I would like to know how to find the terms 11 12 and tell me de formula the array is:
23 03 01 05 03 08 02 06 03 06
24 04 08 09 04 25 13 15 05 08
26 09 19 12 06 31 22 29 16 21
31 10 24 22 15 32 34 33 27 24
32 32 25 33 30 34 35 34 31 35 Answered by Janice Cotcher. 





Proof of a Unique Solution 
20090724 

From muele: Find matrix A such that A is not invertible, and
b such that Ax=b has a unique solution Answered by Robert J. Dawson. 





Finding an Array to an Integer Linear Programming Problem 
20090512 

From Debbie: how to make an array for 3 box of juice for 25 students and 2 teacher. 1 pack of juices
hols 3boxes the answer is 9 packages but how do you make array for this Answered by Janice Cotcher. 





A linear system 
20090313 

From Rasanga: Use the row echelon form of the augmented matrix to solve the following linear system.
X1+2X2+X4=6
X3+6X4=7
X5=1 Answered by Harley Weston. 





Augmented matrix: independent, dependent, or inconsistent? 
20090223 

From Anna: Perform row operations on the augmented matrix as far as necessary to determine whether the system is independent, dependent, or inconsistent.
x + y + z = 11
x  y + 3z = 5
2x + 2y + 2z = 15 Answered by Harley Weston. 





The column space of a matrix 
20090212 

From John: Question from John, a student:
A=
1 1 0 0
1 1 0 0
0 0 1 0
0 0 1 1
B=
1 5 6
1 5 6
0 7 2
0 0 9
Is the space spanned by the columns of A the same as the space spanned by the columns of B? Answered by Harley Weston. 





Using the augmented matrix 
20081017 

From Karlena: I am supposed to write the augmented matrix of the system and use the matrix method to solve the system. I must show my work algebraically
x+y+2z=30
2x+3y+2z=53
x+2y+3z=47 Answered by Harley Weston. 





A linear system 
20080823 

From dipesh: consider the system of equations
x6y+2z=5
2x9yz=14
4x+12y3z=19 by reducing the augm matrix to row echelon form, find
the solution to the equation.
leaving the first two equations the third is changed to 3x+6y+14z=31
show the equations have infinitely many solutions and give a general
formula for them Answered by Penny Nom. 





solving four simultaneous equations 
20080718 

From Muhammad: 2B2C+4E=1
A+B+C+D=0
2B2C2D+E=0
B+C+4D2E=0 Answered by Janice Cotcher. 





Determinants 
20080502 

From Henry: I have a question about solving 3x3 matrices.
The traditional way, or at least the way I've been taught, is that if one has a 3x3 matrix such as:
[ a b c ]
[ d e f ]
[ g h i ]
one solves it according to this formula:
[ei  hf)  (bi  hc) + (bf  ec) = determinant.
According to a book I'm now studying to prepare for the California CSET exam, there is another, easier, way to solve it:
[ a b c ] [ a b ]
[ d e f ] [ d e ]
[ g h i ] [ g h ]
In other words, one repeats the first two rows of the matrix and adds them to the right.
At this point, the determinant is calculated thus:
(aei) +(bfg) + (cdh)  (gec)  (hfa)  (idb).
Is this, in fact, correct? Answered by Harley Weston. 





Matrix multiplication 
20080408 

From manashi: i. why matrix division is not possible?
ii.when we add or subtract two matrix , getting the result by addind or subtracting correspondind elements....but in case of multiplication it is not but why? Answered by Harley Weston. 





Row echelon form 
20080221 

From cOCO: USE ELEMENTARY ROW OPERATIONS TO WRITE THE MATRIX BELOW IN ROW
ECHELON FORM.
1 1 8  2
2 1 1 11
2 1 14 11 Answered by Penny Nom. 





Animals for sale 
20071209 

From Marion: This question has come up and I know the answer and the equation, but how do you solve this?
Please share the proof. cows=$10, pigs=$3, chickens=$.50
In any combination buy 100 animals with $100. Answered by Leeanne Boehm. 





An augmented matrix 
20071129 

From Beth: I am having troubles fiinding this augnmented matrix. I know how to do it
but everytime i do it it get a different answer and its not the right answer.
Could you help me to make sure I do it right?
Here is the problem:
4x  3y = 5
2x +9y = 6 Answered by Harley Weston. 





Area of a 17sided lot 
20071121 

From Lynda: My uncle is wanting to buy this piece of land [a 17sided polygon] but we are questioning the acerage total. the measurements are [on the attached diagram]. Answered by Stephen La Rocque. 





A matrix equation 
20071116 

From stephanie: Im supposed to solve
( 1 tan =E8/2) ( 1 tan =E8/2)^(1)
(tan =E8/2 1 ) (tan =E8/2 1 )
Matrix AA<(1)=I Answered by Penny Nom. 





Linear systems and inverses 
20070806 

From Marsia: explain how inverses are used to solve linear systems. Answered by Penny Nom. 





A matrix of polynomials 
20070718 

From Mac: can you please help me out to solve this ?
Let A be a n*n matrix, the elements of which are real (or complex) polynomial in x.
If r rows of the determinant becomes identical when x=a, then the determinant
A) has a factor of order r
B) has a factor or order > r
C) has no factor
D) has a factor of order < r Answered by Harley Weston. 





An augmented matrix 
20070213 

From Mary: I've been trying for quite some time now to figure this out. I have to solve this by using the GaussJordan Method: 3x  y = 15 2x + 3y = 10 Can anyone help me? Answered by Penny Nom and Gabriel Potter. 





Nickels, dimes and quarters 
20070205 

From Avinash: Mary has 48 coins made up of nickels, dimes and quarters with a total value of $5.10. She has 4 more dimes than nickels and quarters combined. How many coins of each kind does she have? Use matrix to solve the system Answered by Stephen La Rocque. 





Induction 
20061031 

From Ross: Suppose that A and B are square matrices with the property AB= BA. Show that AB^n = B^n A for every positive integer n. Answered by Stephen La Rocque and Penny Nom. 





A matrix equation 
20061014 

From Ngozi: If I have AB = C, where A and C are both 1x6 matrixes and B is a 6x6 matrix, how can I solve for B by dividing C over A? Answered by Chris Fisher. 





Who is taller: John or Mary? 
20050914 

From Ulises: All the students in a school are arranged in a rectangular array. After that, the tallest student in each row was chosen, and then among these John Smith happened to be the shortest.Then, in each column, the shortest student was chosen, and Mary Brown was the tallest of these. Who is taller: John or Mary? Answered by Penny Nom and Claude Tardif. 





A matrix problem 
20050404 

From Alan:
Let A = 

1  1  0 

2  1  2 
a  b  c 
where a, b, c are constant real numbers. For what values of a, b, c is A invertible? [Hint: Your answer should be an equation in a, b, c which satisfied if and only if A is invertible.]
Answered by Judi McDonald. 





Two matrix problems 
20050330 

From Sue: Question 1
Suppose all matrices in the equation below are square and invertible. Solve for x .
BA1XB1 + 2BA + In = 0 (the symbol "0" here denotes the matrix of all 0's in it)
Also, A1 or B1 is indicating inverse and "In" = for example, A1 times A
I hope you understand the above. I have to show all the steps.
Question 2
Suppose we consider the set of all 2x2 matrices along with the operations of matrix addition and multiplication. Do they form a field? Why or why not?
I think the answer is no because under multiplication it is not commutative and not all square matrices are invertible. I not positive so I'd like some help. Answered by Penny Nom. 





A matrix construction problem 
20050314 

From Marcelo: I want to know if is it possible to solve this problem:
I have an empty NxM matrix and I know totals (sum) by rows and totals by column.
Is there any algorithm to fill the matrix so that the summary of columns and rows gives the original values I have? Answered by Harley Weston. 





Pizza for Jack? 
20040916 

From Grace: Jack is playing pool with Jim for $1 a game. He has only $2 and decides to play until he goes broke or has $5, at which point he will quit and go out for a pizza with Jim(Dutch treat). Jack knows from past experience that he beats Jim 60% of the time. What is the probability that Jack will get to eat pizza? Hints: Let A be the 6x6 matrix defined by A=[aij], where aij is the probability that Jack will have $(i1)after one game is he starts with $(j1). For example, a23  .40 since there is a 40% probability that Jack will end up with $1 after a game is he starts the game with $2 (If Jack wins 605 of the time, he must lose 40% of the time). Also, for example, a52 = 0 since there is no way jack can have $4 after one game if he had $1 at the beginning of the game. Since Jack will stop if he goes broke or accumulates $5, a11 and a66 are both 1.
Let x0 = [0 0 1 0 0 0 ] transposed, which we interpret as saying that initially Jack has $2 with a probability 1. Then Ax0 will represent the porbability of each amount of money, $0$5, after one game. What is the probability that Jack will be able to eat pizza by computing Akx0 for large k and finding a limiting value. Answered by Penny Nom. 





Row echelon form 
20040724 

From Michael: My name is Michael and I'm in the 11th grade. I have a Math question that I can't solve. The problem is system of equations that I need to do in augmented matrix form, find the row echelon form, and solve it by using back substitution.
2x + 3y + 7z =13
3x + 2y  5z = 22
5x+ 7y  3z = 28 Answered by Penny Nom. 





Arrays 
20040219 

From A parent: please demonstrate mathematical arrays fro a 3rd grader Answered by Penny Nom. 





Matrices 
20031205 

From Julie: I am doing a project and need to find some mathematiciens who had an influence in matrices. I can't seem to find any when I search online. Could you please help me with this? Answered by Judi McDonald. 





A determinant 
20030213 

From A student:
I have to find the determinant of the following matrix 2  3  1  2  4  3  0  2  5  1  4  2  1  3  5  2  3  4  1  2  6  0  3  2  4  Answered by Penny Nom. 





Augmented matrix 
20021231 

From Michelle: I am trying to augment a matrix so that i can find the values of the variables a, b, and c. For the life of me i can't find a solution to the matrix: 3 5 2 ' 22 2 3 1 ' 9 4 3 3 ' 1 I thank you for your help, Michelle Answered by Penny Nom. 





An augmented matrix 
20020420 

From A student: Hi my math teacher asked us to solve an augmented matrix. I am in twelfth grade and need help. The book we are working on is college algebra. Here it is a+2b+c=0 2a+5b+4c=1 ab9c=5 Answered by Penny Nom. 





If the matrix A is inverible and AB =AC, then B = C 
20020327 

From Vikki: i hope you can help i am soooo stuck here goes: a)
A= 0 1 B= 1 1 c= 2 5 0 2 3 4 3 4
A,B and c are matrices Evaluate AB and Ac (which I can do) then
b) I need to prove that if the matrix A is inverible and AB =AC, then B = C. Why does this not contradict what happened in part a)? Answered by Leeanne Boehm. 





Matrix 
20011121 

From Hoda: I have a question about matrix multiplication; well, actually, matrix division. I am assuming that matrices are divided the same as they are multiplied; that is, row by column. But what happens if you have to divide by zero? How does this affect the resulting matrix? Answered by Patrick Maidorn and Penny Nom. 





Conformable matrices 
20010805 

From Wayne: Can someone explain the concept of conformable matrices in a way that is easy to understand ? One definition says to multiply matrices rows and columns must conform, ie, 5 x 3 matrix times a 3 x 5 matrix. In the next example, however a 8 x 1 matrix and a 8 x 3 matrix are said to be conformable! Answered by Steve Kirkland. 





Matrix reconstruction 
20010719 

From Guy: Is there a way to get the sums of rows, columns and diagonals of an n x n matrix to reconstruct the original matrix? Answered by Walter Whiteley and Patrick Maidorn. 





Matrices 
20010326 

From Peg: What are some applications of matrices, basic trigonometry, and linear systems in the real world? I'm writing and Algebra report about where these topics are used outside of the classroom. Answered by Judi McDonald and Walter Whiteley. 





Solving Equations 
20010223 

From Stephanie: Do you know who came up with solving equations? Do you have any websites that can give me good information on solving equations? Do you know any history on solving equations? Do you know what solving equations is used for? And finally............Sorry about all of the questions :) Has the form of solving equations changed from the time it came out to now? Answered by Juci McDonald. 





Where will we use this in the real world? 
20001011 

From Jane Ann Musgrove: As a teacher of mathematics, I am always asked "Where will we use this in the real world?". I am seeking ideas/sites via the internet where students can find answers to this type of question. Can you help me? To be more specific, right now I am interested in finding careers where the employees would use the concepts of "Radicals", "Matrices", and "Logarithms". This information will be used by students to make presentations to the class on their findings from internet searches. Answered by Harley Weston. 





A matrix equation 
20000514 

From A student: Right now, we are dealing with matrices and we are supposed to solve the following problem on our graphingcalculators: 2a+3b4c+d=20 a2b+3c5d=14 3a+4b2c+3d=19 5ab+6c+4d=5 Answered by Penny Nom. 





Matrices Information 
20000502 

From William Avery: I am an OAC student at Governor Simcoe Secondary School in St. Catharines Ontario. Today at school we were handed an independent study project by our Finite teacher. This assignment is based on Matrices, it involves performing some simple matrix calculations, but also involves a written section. This written section asks for the following: . . . Answered by Marley Weston. 





Taxis in Chicago 
20000327 

From A high school studenthigh school student: Suppose that taxis pick up and deliver passengers in Chicago, which is divided into three zones. Records kept by the drivers show that of the passengers picked up in Zone 1, 50% are taken to a destination in Zone 1, 40% to Zone 2, and 10% to Zone 3. OF the passengers picked up in Zone 2, 40% go to Zone 1, 30% to Zone 2, and 30% to Zone 3. Of the passengers picked up in Zone 3, 20% go to Zone 1, 60% to Zone 2 and 20% to Zone 3. Suppose that at the beginning of the day, 600 of the taxis are in Zone 1, 100 in Zone 2, and 300 in Zone 3. What is the distribution of taxis in the various zones after all have had two riders? Answered by Harley Weston. 





A system of equations in five unknowns 
20000320 

From Will: I have been having some problem with the following question for some time. I would appreciate any help on solving the problem or a solution. Q: Assume that a system of equations in the unknowns x1, x2, x3, x4 and x5 when converted to row echelon form gives . . . Answered by Penny Nom. 





Matricies 
19981126 

From Stephanie Webster: If a matrix for a rectangle looks this way: AACC BDDB What does the matrix for a square look like? Answered by Penny Nom. 





Mathematical Arrays 
19980501 

From Gene Lanctot: Could someone please explain what a mathematical or arithmetical array is? The array in question is used in grade three math in Ontario. I would also like to know what its purpose is. Answered by Harley Weston. 





Logic and Matrix Instruction 
19980424 

From Robin Booker: I need assistance with instruction strategies to teach the construction of a matrix, solving a logic problem. Providing instruction in the construction of a simple matrix , no problem. However, I stumpted on this one. Five players were chosen as All Stars at the basketball banquet. Based on the following clues, find the player's name, team, uniform color and number of points scored.... Answered by Harley Weston. 





Matrices 
19980310 

From Ksya:
 A and B are matrices. If A^n=B^n, can we say A=B or det(A)=det(B) or det(A)^n=det(B)^n ? Any conditions ???
 If B^(1) is the inverse of B, where B is a matrices. Can we say [(B^(1))^n][B^n]=I, where I is identity matrices? Any conditions???
Answered by Doug Farenick. 





Matrice 
20060201 

From Kader: mon probleme est le suivant soit deux matrices carrees A et B d'ordre n qui sont anticommutatives AB= BA , demontrer que au moins une des deux matrices n'est pas inversible si n est impair.
je n'arrive pas a utiliser le fait que n soit impair, trouver le rapport entre n impair et inverse des matrices, je pars sur la base de DETAB=DETA*DETB Answered by Claude Tardif. 

