Find the inverse matrix for the given matrix.
$\begin{array}{l} [\begin{array}{cc} - 14 & - 13 \\ - 9 & - 8 \end{array}] \\ A^{- 1} = ? \end{array}$

Answer

Expert–verified

Hide Steps

Answer

Final Answer: The inverse of the given matrix is $[\begin{matrix} 1.6 & - 2.6 \\ - 1.8 & 2.8 \end{matrix}]$

Steps

Step 1 ：We are given the matrix A = $[\begin{matrix} - 14 & - 13 \\ - 9 & - 8 \end{matrix}]$

Step 2 ：The inverse of a 2x2 matrix $[\begin{matrix} a & b \\ c & d \end{matrix}]$ is given by $\frac{1}{a d - b c} [\begin{matrix} d & - b \\ - c & a \end{matrix}]$

Step 3 ：First, we need to calculate the determinant (ad-bc) of the given matrix. The determinant of matrix A is -4.999999999999988

Step 4 ：Since the determinant of the matrix A is not equal to zero, the matrix is invertible

Step 5 ：Applying the formula for the inverse of a 2x2 matrix, we get the inverse of the matrix A as $[\begin{matrix} 1.6 & - 2.6 \\ - 1.8 & 2.8 \end{matrix}]$

Step 6 ：Final Answer: The inverse of the given matrix is $[\begin{matrix} 1.6 & - 2.6 \\ - 1.8 & 2.8 \end{matrix}]$

Find the inverse matrix for the given matrix.[−14−13−9−8]A−1=?

Answer

Popular Problems

Find the inverse matrix for the given matrix.
$\begin{array}{l} [\begin{array}{cc} - 14 & - 13 \\ - 9 & - 8 \end{array}] \\ A^{- 1} = ? \end{array}$