Kye

2021-03-02

Find the inverse of matrices

$\left[\begin{array}{cc}8& 6\\ 5& 4\end{array}\right]$

Nathaniel Kramer

Skilled2021-03-03Added 78 answers

Step 1

here given matrix

$A=\left[\begin{array}{cc}8& 6\\ 5& 4\end{array}\right]$

Use the formula for$2\times 2$ matrices, which states

if$A=\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$

Thus${A}^{-1}=\frac{1}{ad-bc}\left[\begin{array}{cc}d& -b\\ -c& a\end{array}\right]$

Step 2

Thus

${A}^{-1}=\frac{1}{2}\left[\begin{array}{cc}4& -6\\ -5& 8\end{array}\right]$

$=\left[\begin{array}{cc}2& -3\\ \frac{-5}{2}& 4\end{array}\right]$

here given matrix

Use the formula for

if

Thus

Step 2

Thus

Jeffrey Jordon

Expert2022-01-29Added 2605 answers

Answer is given below (on video)

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