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Linear Algebra

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Socks-Shoes Example

LINALG-NYV8HX

Let:

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

Find $A^{-1}$, if it exists.

A

$\begin{pmatrix}1&0&0\\\ 0&1&-1\\\ 0&0&01\end{pmatrix}$

B

$\begin{pmatrix}\cfrac{1}{2}&0&0\\\ 0&-\cfrac{1}{3}&0\\\ 0&0&01\end{pmatrix}$

C

$\begin{pmatrix}\cfrac{1}{2}&0&0\\\ 0&-\cfrac{1}{3}&-1\\\ 0&0&1\end{pmatrix}$

D

$\begin{pmatrix}\cfrac{1}{2}&0&0\\\ 0&-\cfrac{1}{3}&\cfrac{1}{3}\\\ 0&0&1\end{pmatrix}$

E

The matrix $A$ is not invertible