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 Sujet: determinant
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Matrice 2006-02-01
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
Claude Tardif lui répond.
The evaluation of a 3 by 3 determinant 2016-02-19
Kristen pose la question :
What is the step-by-step process on how to evaluate the determinant of a 3*3 matrix, using the expansion method (not the diagonal method)
Penny Nom lui répond.
The adjacency matrix of an undirected graph 2010-01-15
Bhavya pose la question :
Let Cn be the undirected graph with vertex set V = {1,2,3,...,n} and edge set E = {(1,2), (2,3), (3,4),.... , (n-1,n), (n,1)}. Let An be the adjacency matrix of Cn.
a. Find the determinant of An.
b. Find (An)^2

Robert Dawson lui répond.
4 by 4 determinants 2008-06-27
rav pose la question :
How to solve problems of determinants which has four rows and four columns& please give me easy tips to solve permutations and combinations problems.
Harley Weston lui répond.
Determinants 2008-05-02
Henry pose la question :
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?

Harley Weston lui répond.
Area of a 17-sided lot 2007-11-21
Lynda pose la question :
My uncle is wanting to buy this piece of land [a 17-sided polygon] but we are questioning the acerage total. the measurements are [on the attached diagram].
Stephen La Rocque lui répond.
A matrix of polynomials 2007-07-18
Mac pose la question :

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

Harley Weston lui répond.
Evaluating a determinant 2007-02-25
Suud pose la question :
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
Haley Ess lui répond.
A matrix problem 2005-04-04
Alan pose la question :
 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.]

Judi McDonald lui répond.
A determinant 2003-02-13
A student pose la question :

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

Penny Nom lui répond.
Expanding determinants using minors 2001-02-20
A student pose la question :
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 |

Harley Weston lui répond.
order 4+ determinants 1999-12-06
Joe Kron pose la question :
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.
Walter Whiteley lui répond.
Area of a triangle from vertex coordinates 1999-04-21
Mark Tyler pose la question :
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((x1-x2)*(y1-y3)-(y1-y2)*(x1-x3)) 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.
Walter Whitley lui répond.

Intersection of Planes 1998-12-03
Lindsay Fear pose la question :
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

Walter Whiteley lui répond.

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