Questions: Let A=[[4, 3, -5], [8, 1, 5], [-9, -6, 9]] Let B=A^-1. What is the value of b23? If B does not exist, enter 99999 as your answer.

Transcript text: Let $A=\left[\begin{array}{ccc}4 & 3 & -5 \\ 8 & 1 & 5 \\ -9 & -6 & 9\end{array}\right]$ Let $B=A^{-1}$. What is the value of $b_{23}$ ? If B does not exist, enter 99999 as your answer.

Solution

Solution Steps

Step 1: Check Invertibility

The determinant of matrix A is -7.577272143066663\times 10^{-15}, indicating that A is invertible.

Step 2: Calculate Inverse

The inverse matrix B is calculated using the numpy.linalg.inv function. Matrix A: [[ 4 3 -5] [ 8 1 5] [-9 -6 9]] Inverse Matrix B: [[-5.14697100\times 10^{15} -3.95920846\times 10^{14} -2.63947231\times 10^{15}] [ 1.54409130\times 10^{16} 1.18776254\times 10^{15} 7.91841693\times 10^{15}] [ 5.14697100\times 10^{15} 3.95920846\times 10^{14} 2.63947231\times 10^{15}]]

Step 3: Extract Desired Entry

The value of the entry at indices (1, 2) in the inverse matrix B is 7918416927244827.