Given matrices A = (begin{bmatrix} 2 & 3 4 & 7 end{bmatrix}) and B = (begin{bmatrix} 1 2 end{bmatrix}), solve for X in the system of equations AX = B using the inverse matrix method.

Question

Given matrices A = (begin{bmatrix} 2 & 3  4 & 7 end{bmatrix}) and B = (begin{bmatrix} 1  2 end{bmatrix}), solve for X in the system of equations AX = B using the inverse matrix method.

Accepted Answer

Step:1 ：1. First, we need to find the inverse of matrix A, denoted as A^{-1}. The formula for a 2x2 matrix is (frac{1}{ad - bc}) (begin{bmatrix} d & -b  -c & a end{bmatrix}).Step:2 ：So, the inverse of A, A^{-1}, is (frac{1}{2*7 - 3*4}) (begin{bmatrix} 7 & -3  -4 & 2 end{bmatrix}) = (begin{bmatrix} 7 & -3  -4 & 2 end{bmatrix}).Step:3 ：2. We can solve for X by multiplying A^{-1} by B. Therefore, X = A^{-1}B.Step:4 ：Thus, X = (begin{bmatrix} 7 & -3  -4 & 2 end{bmatrix}) (begin{bmatrix} 1  2 end{bmatrix}) = (begin{bmatrix} 7*1 - 3*2  -4*1 + 2*2 end{bmatrix}) = (begin{bmatrix} 1  0 end{bmatrix}).

Answer

Step: 1 ：1. First, we need to find the inverse of matrix A, denoted as A^{-1}. The formula for a 2x2 matrix is (frac{1}{ad - bc}) (begin{bmatrix} d & -b  -c & a end{bmatrix}).Step: 2 ：So, the inverse of A, A^{-1}, is (frac{1}{2*7 - 3*4}) (begin{bmatrix} 7 & -3  -4 & 2 end{bmatrix}) = (begin{bmatrix} 7 & -3  -4 & 2 end{bmatrix}).Step: 3 ：2. We can solve for X by multiplying A^{-1} by B. Therefore, X = A^{-1}B.Step: 4 ：Thus, X = (begin{bmatrix} 7 & -3  -4 & 2 end{bmatrix}) (begin{bmatrix} 1  2 end{bmatrix}) = (begin{bmatrix} 7*1 - 3*2  -4*1 + 2*2 end{bmatrix}) = (begin{bmatrix} 1  0 end{bmatrix}).

Given matrices A = $[\begin{matrix} 2 & 3 \\ 4 & 7 \end{matrix}]$ and B = $[\begin{matrix} 1 \\ 2 \end{matrix}]$ , solve for X in the system of equations AX = B using the inverse matrix method.

Answer

Popular Problems

Given matrices A = [2347] and B = [12], solve for X in the system of equations AX = B using the inverse matrix method.

Answer

Popular Problems

Given matrices A = $[\begin{matrix} 2 & 3 \\ 4 & 7 \end{matrix}]$ and B = $[\begin{matrix} 1 \\ 2 \end{matrix}]$ , solve for X in the system of equations AX = B using the inverse matrix method.