Question

HELP PLEASEE

Answer 1

onsider the following invertible matrix A, and vector B.

A  = 
2 10 4 3 8
2 10 3 3 3
9 11 9 3 6
5 8 3 1 3
4 7 5 10 6

B =
10
10
11
8
7
.

Use Cramer's Rule to solve the following.

(a) Solve the equation AX = B for the variable x1 .
(b) Solve the equation AX = B for the variable x2 .

Answer 2

assume matrix A and B have square brackets around the entries

Answer 3

any suggestions would help....

Answer 4

First, evaluate the "determinant" of matrix "A." May I assume that you know how to do that? If not, ask for clarification.
To find the variable x1, we throw out the first COLUMN of A and replace it with B. We evaluate the determinant of the resulting matrix.
Dividing this numeric result by the determinant of matrix "A" produces the desired value for x1. Find x2 in a similar fashion: replace the 2nd column of A with B, and then evaluate the determinant of this new matrix. Again, divide the result by the determinant of matrix "A."

Answer 5

yes i know hot to find det. but using cramer's rule for b), the minors end up being 4x4 matrices so how do you find the det for that?

Answer 6

@mathmale

Answer 7

rimshaa: Obviously there's a lot of computational work involved in evaluating the determinant of a 5x5 matrix. True, if you use cofactors and minors (as you seem to be doing), you end up with 4x4 matrices. Those can be evaluated in exactly the same way: cofactors and minors. Before I say any more, let me ask you this: has your teacher talked at all about "partitioning" matrices as a way of reducing the drudgery of computation?

Answer 8

rimshaa: Sorry, but I don't see why "using Cramer's Rule for b" poses a problem. Have you used Cramer's rule before? It involves replacing one column (at a time) of [A] with column matrix [B] and then evaluating the determinant of the resulting matrix as you normally would.