







The evaluation of a 3 by 3 determinant 
20160219 

From Kristen: What is the stepbystep process on how to evaluate the determinant of a 3*3 matrix, using the expansion method (not the diagonal method) Answered by Penny Nom. 





Fractions of two quantities 
20160122 

From Melody: Kate ate 1/4 of her orange. Ben ate 2/4 of his banana. Did Kate and Ben eat 3/4 of theit fruit? Explain. Answered by Penny Nom. 





The quadratic formula 
20130103 

From itsel: Find the discriminant ans use it to determine the use the quadratic formula to solve the equasion 2x^2+3x+2=0 Answered by Penny Nom. 





The discriminant 
20100117 

From Sonjonnia: What is the value of the discriminant?
16x^=16x4 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. 





An annuity 
20090227 

From Jules: R 20 000 is deposited in the bank,at the end of each year R 5 000
is withdrawn from it, the interest is 13 percent compounded monthly.
Calculate how many years that person will be able to use his/her money ? Answered by Stephen La Rocque. 





Nullity 
20090216 

From Justin: What exactly does the term nullity mean in the context of transreal numbers invented by Dr. James Anderson?
Thanks for your help in answering this question!
All the Best,
Justin Answered by Robert Dawson. 





4 by 4 determinants 
20080627 

From rav: How to solve problems of determinants which has four rows and four columns& please give me easy tips to solve permutations and combinations problems. Answered by Harley Weston. 





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. 





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 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. 





Values of k for which k(x^2+2x+3)  4x  2 is never negative 
20070629 

From claire: Find the range of values of k for which k(x^2+2x+3)  4x  2 is never negative. Answered by Harley Weston. 





The roots of (x  k)(13x) + 1 = 0 
20070628 

From Claire: Show that the roots of (x  k)(13x) + 1=0 are real and distinct for all real values of k. Hence, or otherwise, find the range of 9sin^2 r  6sin r + 13 Answered by Harley Weston. 





Evaluating a determinant 
20070225 

From Suud: Please send me the detailed steps of calculating the determinant of the following 4by4 matrix 1 3 1 2 2 0 1 1 3 2 0 4 0 3 1 2 Answered by Haley Ess. 





My wife's recent pregnancy, 
20060724 

From Tom: During my wife's recent pregnancy, it so happened that my wife's 29th birthday fell on the exact same day that her unborn child was 29 weeks old (i.e. it was 29 x 7 days from the date of conception as advised by the doctor)
I would like to know what the probability is of the above event occurring for a randomly chosen pregnant woman i.e. that the pregnant mum's x'th birthday falls on the same day that the unborn child is x weeks old EXACTLY.
Answered by Stephen La Rocque. 





Discriminant 
20050620 

From A student: If a quadratic has real root, its discriminant b24ac>=0 Is there any similar condition or method by which you can find whether roots of a cubic equation are real or not? Answered by Chris Fisher. 





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. 





Trading fish for bread 
20050225 

From Mike: Byron lives where people trade goods they produce for other things they
need. He has some fish and wants to trade them for bananas. He finds
the following:
5 fish = 2 loaves of bread
6 oranges = 2 melons
1 loaf of bread = 1 banana and 3 oranges
4 loaves of bread = 14 oranges
How many bananas can Byron get with 5 fish? Answered by Penny Nom. 





A metric prefix table 
20040307 

From April: Can you tell me what the scale is for nano, micro, mega, kilo, etc.... I know that mega is 10 to the sixth power but I can't remember the other ones. Answered by Penny Nom. 





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. 





Expanding determinants using minors 
20010220 

From A student: Question: 1) Determinants by expansion by minors. i)  1 2 1 2 1   1 0 0 1 0   0 1 1 0 1   1 1 2 2 1   0 1 1 0 2  Answered by Harley Weston. 





Banana yogurt 
20001103 

From James: A grocery store has 100 cartons of banana yogurt in stock.Each carton contains 12 cup of banana yogurts.The probability that a cup has fewer than 20 banana chunks in it is 10 %. So,What is the probability that between 15 and 25 (inclusive) cartons out of the 100 cartons have exactly 3 cups with fewer than 20 banana chunks? Answered by Harley Weston. 





Transporting bananas 
20001018 

From Krystie: A farm has 45 bananas, a man has to take a truck and transport 15 bananas to a market that is 15 miles away. Every mile he travels, he must eat a banana. I have to get at least one banana to the market Answered by Penny Nom. 





Rule of 78 
20000322 

From Dan Baumgarten: Can you explain the rule of 78 and the reverse rule of 78? Thanks. Answered by Claude Tardif. 





order 4+ determinants 
19991206 

From Joe Kron: Why is it never shown how to calculate the value of 4x4 (or larger size) deteminants by the diagonal multiply methods that are generally shown for 2x2 and 3x3 determinants? The method I'm talking about is called Cramer's Rule??? Is this method not extensible to order 4+ and if not why not? Anyway the method always shown for order 4+ is called "reduction by minors" which is not the answer to this question. Answered by Walter Whiteley. 





Camels and bananas 
19991202 

From Marie Rich: Corey Camel's harvest, worth its weight in gold, consists of 3000 bananas. The market place where the stash can be cashed in is 1000 miles away. However, Corey must walk to the market, and can only carry up to 1000 bananas at a time. Furthermore, being a camel, Corey eats one banana during each and every mile she walks (so Corey can never walk anywhere without bananas). How many bananas can Corey get to the market? Answered by Claude Tardif. 





Area of a triangle from vertex coordinates 
19990421 

From Mark Tyler: I'm no schoolkid, but I liked your answers about triangles. You might enjoy a quick look at this, the kids may too. I was working on a Voronoi dual where I had to calculate the areas of very many triangles expressed as vertex coordinates, so I derived the following very direct formula: A = abs((x1x2)*(y1y3)(y1y2)*(x1x3)) for triangle (x1,y1)(x2,y2)(x3,y3) I've never seen this in a textbook. Is it original? I doubt it, the proof is only a few lines long. Regardless, it may be fun for the kids, even if it's not on the curriculum. Answered by Walter Whitley. 





Intersection of Planes 
19981203 

From Lindsay Fear: My name is Lindsay Fear. I am an OAC student (which is the Ontario equivalent to Grade 12 in most other states and provinces). I am in an Algebra and Geometry course and am currently studying a unit on equations of planes. Our teacher has given us this question that my friend and I have attempted several times, but we are still unable to solve it. My teacher has also suggested using the internet as a resource. The question is: Prove that a necessary condition that the three planes x + ay + bz = 0 ax  y + cz = 0 bx + cy  z = 0 have a line in common is that a^2 + b^2 + c^2 + 2abc = 1 Answered by Walter Whiteley. 





il y a deux contenant 
20070123 

From Eric: il y a deux contenant un de 3 litre et un de 5 litre les deux sont vide comment en les remplisant on peux obtenire 4 litre Answered by Claude Tardif. 





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. 

