MHB Find the General Expression for a Linear Transformation

Leanna
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I don't quite get this question, how is it done ?
 

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Hi Leanna,

It is asking you to compute the matrix product $$\begin{pmatrix}-1&-2&0&1\\0&3&1&1\\2&0&2&-4\\0&-1&0&0\end{pmatrix}\begin{pmatrix}r\\s\\t\\u\end{pmatrix}$$
 
Can you see if answer to first question is (-r, 3s, 2t, u)?

Or is it
Idk how to use latex but it's one matrix
(-r -2s+u)
(3s+t+u)
(2r+2t-4u)
(. -s. )
 
Leanna said:
Can you see if answer to first question is (-r, 3s, 2t, u)?

Or is it
Idk how to use latex but it's one matrix
(-r -2s+u)
(3s+t+u)
(2r+2t-4u)
(. -s. )

According to an online matrix calculator I found:

$$\left(\begin{array}{c}-1 & -2 & 0 & 1 \\ 0 & 3 & 1 & 1 \\ 2 & 0 & 2 & -4 \\ 0 & -1 & 0 & 0 \end{array}\right)\left(\begin{array}{c}r \\ s \\ t \\ u \end{array}\right)=\left(\begin{array}{c}-r-2s+u \\ 3s+t+u \\ 2r+2t-4u \\ -s \end{array}\right)\quad\checkmark$$
 
Thanks a lot
 

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