Linear Algebra

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Moderate

Simultaneous Determinant and Inverse

LINALG-EVJRSV

If:

$$A=\begin{pmatrix} 1 & 0 & 2 \\\ 2 & -1 & 3 \\\ 4 & 1 & 8\end{pmatrix}$$

...then:

A

$A^{-1}=\begin{pmatrix} 11 & -2 & 2 \\\ -4 & 0 & 1\\\ 6 &-1 & -1\end{pmatrix}$ and $\det(A)=1$

B

$A^{-1}=\begin{pmatrix} -11 & 2 & 2 \\\ -4 & 0 & 1\\\ 6 &-1 & -1\end{pmatrix}$ and $\det(A)=1$

C

$A^{-1}=\begin{pmatrix} -11 & 2 & 2 \\\ 4 & 0 & -1\\\ 6 &-1 & -1\end{pmatrix}$ and $\det(A)=-1$

D

$A^{-1}=\begin{pmatrix} -11 & 2 & 2 \\\ -4 & 0 & 1\\\ 6 &-1 & -1\end{pmatrix}$ and $\det(A)=-1$