Solve the matrix equation AX =B for X using

A=[2-3]
[1 5]

B=[4 ]
[2 ]

so you didn't like my answer ?

http://www.jiskha.com/display.cgi?id=1248386856

No its not that I'm trying to write it exactly how I got it on my sheet but when I sumbit it it comes out a little different but I guess you understood it.

To solve the matrix equation AX = B for X, we can use the formula X = A^(-1) * B, where A^(-1) represents the inverse of matrix A.

Step 1: Calculate the inverse of matrix A.

The inverse of matrix A can be found using the formula A^(-1) = (1/det(A)) * adj(A), where det(A) represents the determinant of matrix A, and adj(A) represents the adjugate of matrix A.

First, calculate the determinant of matrix A:

det(A) = (2 * 5) - (-3 * 1) = 10 + 3 = 13

The determinant of A is 13.

Next, calculate the adjugate of matrix A:

adj(A) = [5 3]
[-1 2]

Step 2: Calculate A^(-1) using the formula A^(-1) = (1/det(A)) * adj(A):

A^(-1) = (1/13) * [5 3] = [5/13 3/13]
[-1 2] [-1/13 2/13]

Step 3: Multiply A^(-1) by matrix B to find X:

X = A^(-1) * B

= [5/13 3/13] * [4] = [5/13 * 4 + 3/13 * 2] = [20/13 + 6/13] = [26/13] = [2]
[-1/13 2/13] [2] [-1/13 * 4 + 2/13 * 2] [-4/13 + 4/13] [0]

Therefore, the solution to the matrix equation AX = B is X = [2] and [0].