Question

Find the inverse of matrices begin{bmatrix}8 & 6 5 & 4end{bmatrix}

Matrices
ANSWERED
asked 2021-03-02
Find the inverse of matrices
\(\begin{bmatrix}8 & 6 \\5 & 4\end{bmatrix}\)

Answers (1)

2021-03-03
Step 1
here given matrix
\(A=\begin{bmatrix}8 & 6 \\5 & 4\end{bmatrix}\)
Use the formula for \(2 \times 2\) matrices, which states
if \(A=\begin{bmatrix}a & b \\c & d \end{bmatrix}\)
Thus \(A^{-1}=\frac{1}{ad-bc}\begin{bmatrix}d & -b \\-c & a \end{bmatrix}\)
Step 2
Thus
\(A^{-1}=\frac{1}{2}\begin{bmatrix}4 & -6 \\-5 & 8 \end{bmatrix}\)
\(=\begin{bmatrix}2 & -3 \\\frac{-5}{2} & 4 \end{bmatrix}\)
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