$A=\left[\begin{array}{cc}4& 8\\ -5& -10\end{array}\right]$

The inverse, ${A}^{-1}$, is A=?

prkosnognm
2022-07-29
Answered

Find the inverse of the following matrix A, if possible. Check that $A\ast {A}^{-1}$ and ${A}^{-1}\ast A=I$

$A=\left[\begin{array}{cc}4& 8\\ -5& -10\end{array}\right]$

The inverse, ${A}^{-1}$, is A=?

$A=\left[\begin{array}{cc}4& 8\\ -5& -10\end{array}\right]$

The inverse, ${A}^{-1}$, is A=?

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Reese King

Answered 2022-07-30
Author has **13** answers

determinant matrix A = 4*-10 - 8*-5 = 0 => inconsistentmatrix => answer is not exist

Ashlyn Krause

Answered 2022-07-31
Author has **4** answers

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

$\frac{1}{-40-(-40)}=\frac{1}{0}$

Therefore there is no ${A}^{-1}$ so:

$\left[\begin{array}{cc}N& N\\ N& N\end{array}\right]$

$\frac{1}{-40-(-40)}=\frac{1}{0}$

Therefore there is no ${A}^{-1}$ so:

$\left[\begin{array}{cc}N& N\\ N& N\end{array}\right]$

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