Hi !(adsbygoogle = window.adsbygoogle || []).push({});

I am a little bit confused with notation in the following:

Let A=

[tex]\begin{bmatrix}

2 & 3 & 4 \\

8 & 5 & 1 \\

\end{bmatrix}[/tex]

and consider A as a linear transformation mapping [tex]\mathbb{R}^3[/tex] to [tex]\mathbb{R}^2[/tex]. Find the matix representation of A with respect to the bases

[tex]\begin{bmatrix}

1\\

1\\

0\\

\end{bmatrix} , [/tex] [tex]\begin{bmatrix}

0\\

1\\

1\\

\end{bmatrix} , [/tex] [tex]\begin{bmatrix}

1\\

0\\

1\\

\end{bmatrix} [/tex] of [tex]\mathbb{R}^3[/tex] and

[tex]\begin{bmatrix}

3\\

1\\

\end{bmatrix} , [/tex] [tex]\begin{bmatrix}

2\\

1\\

\end{bmatrix} [/tex] of [tex]\mathbb{R}^2[/tex]

It seems to be a lot of A´s in here with different meanings, and I suppose it is what confuses me :(. Anyway I solved it as follows:

[tex]\begin{bmatrix}

3 & 2\\

1 & 1\\

\end{bmatrix}^{-1} * [/tex] [tex]\begin{bmatrix}

2 & 3 & 4\\

8 & 5 & 1\\

\end{bmatrix} * [/tex] [tex]\begin{bmatrix}

1 & 0 & 1\\

1 & 1 & 0\\

0 & 1 & 1\\

\end{bmatrix} = [/tex] [tex]\begin{bmatrix}

-21 & -5 & -12\\

34 & 11 & 21\\

\end{bmatrix} [/tex]

I am still not sure that I have not confused myself with all the different A´s :( Am I on the right track or completely lost ?

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# Linear transformation between bases

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