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## Homework Statement

Find A if (2A

^{-1}- 3I)

^{T}=

2*[tex]

\begin{pmatrix}

-1 & 2\\

5 & 4

\end{pmatrix}

[/tex]

## Homework Equations

## The Attempt at a Solution

I have no idea if I'm even on the right track of solving this question...

I simplified the right hand side down to

[tex]

\begin{pmatrix}

-2 & 4\\

10 & 8

\end{pmatrix}

[/tex]

I took the transpose of both sides so the left hand side is just

**(2A**

^{-1}- 3I)The right hand side is now

[tex]

\begin{pmatrix}

-2& 10\\

4 & 8

\end{pmatrix}

[/tex]

I multiplied both sides by A so

LH: A(2A

^{-1}- 3I)

RH: A*[tex]

\begin{pmatrix}

-2& 10\\

4 & 8

\end{pmatrix}

[/tex]

Distribute the A so

LH: (A2A

^{-1}- A3I) =>

**(2I - A3I)**

Bring the A3I part to the right side

LH = 2I

RH = A3I + A*[tex]

\begin{pmatrix}

-2& 10\\

4 & 8

\end{pmatrix}

[/tex]

Simplify the A3I part on the right hand side to get

A * [tex]

\begin{pmatrix}

3 & 0\\

0 & 3

\end{pmatrix}

[/tex]

Factor out the A on the right hand side to get

A * ([tex]

\begin{pmatrix}

-2 & 10\\

4 & 8

\end{pmatrix}

[/tex]

+

[tex]

\begin{pmatrix}

3 & 0\\

0 & 3

\end{pmatrix}

[/tex]

)

Add the two matrices together in the brackets to get

A * [tex]\begin{pmatrix}

1 & 10\\

4 & 11

\end{pmatrix}

[/tex]

So I'm left with

[tex]

\begin{pmatrix}

2 & 0\\

0 & 2

\end{pmatrix}

[/tex]

=

A *

[tex]

\begin{pmatrix}

1 & 10\\

4 & 11

\end{pmatrix}

[/tex]

Now there's no way I can somehow get A like that so I screwed up somewhere in there.. probably from the start lol

This looks so messy... am I allowed to upload my handwritten work on a site then post it here? Seems like a better alternative to the mess I have up there >_> Anyways I'm not really looking for a step by step on how to do this. Just a push in the right direction is all...