Algebra
posted by mike on .
 2 3 5
A= 1 7 9
3 2 10
,
3
B=4
1
I need to solve this matrix equation
AX = B FOR X BY FINDING A^1, given A and B as follows. I am new at this did I write A^1 right? This is suppose to be an A with a minus one at the top.

1kw

Given A and B, where A is a 3x3 matrix, and B is a vector of 3, and
AX=B
To solve for X, we would premultiply by the inverse of A to give
A^{1}A X = A^{1}B
Since A^{1}A is the identity matrix by definition of the inverse, we end up with
X = A^{1}B
To find X, it will be necessary to find the inverse of A, premultiply with B and the result (3x1 vector) will be X as required.
The inverse of A can be found by Gauss elimination, or any other method that you have learned.
The value of X is a multiple or submultiple of [17,4,7].