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 Topic: matrices
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Matrices 2013-11-10
From Ricky:
Why must we have brackets around matrices. Why don't we just neatly write an array of entries cross-wise and up and down to indicate a particular matrix?
Geocaching 2010-10-15
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] = ?

The column space of a matrix 2009-02-12
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?

A linear system 2008-08-23
From dipesh:
consider the system of equations
x-6y+2z=5
2x-9y-z=14
4x+12y-3z=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

Determinants 2008-05-02
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?

Matrix multiplication 2008-04-08
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?

Who is taller: John or Mary? 2005-09-14
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 2005-04-04
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.]

Two matrix problems 2005-03-30
From Sue:
Question 1
Suppose all matrices in the equation below are square and invertible. Solve for x .

BA-1XB-1 + 2BA + In = 0 (the symbol "0" here denotes the matrix of all 0's in it)

Also, A-1 or B-1 is indicating inverse and "In" = for example, A-1 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.

A matrix construction problem 2005-03-14
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?

Arrays 2004-02-19
From A parent:
Matrices 2003-12-05
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?
A determinant 2003-02-13
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

Matrix 2001-11-21
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 2001-08-05
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!
Matrix reconstruction 2001-07-19
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 2001-03-26
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 2001-02-23
From Stephanie:
Do you know who came up with solving equations?
Do you have any web-sites 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?

Where will we use this in the real world? 2000-10-11
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.

A matrix equation 2000-05-14
From A student:
Right now, we are dealing with matrices and we are supposed to solve the following problem on our graphing-calculators: 2a+3b-4c+d=20
a-2b+3c-5d=-14
3a+4b-2c+3d=19
5a-b+6c+4d=-5

Matrices Information 2000-05-02
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:
.
.
.

Taxis in Chicago 2000-03-27
From A high school student high 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?
Matricies 1998-11-26
From Stephanie Webster:
If a matrix for a rectangle looks this way:
`    AACC    BDDB `
What does the matrix for a square look like?

Mathematical Arrays 1998-05-01
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.
Matrices 1998-03-10
From Ksya:
1. 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 ???

2. 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???

Matrice 2006-02-01