MHB Find the General Expression for a Linear Transformation

[Leanna]

View attachment 6275

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

 

[Euge]

Hi Leanna,

It is asking you to compute the matrix product $$\begin{pmatrix}-1&-2&0&1\\0&3&1&1\\2&0&2&-4\\0&-1&0&0\end{pmatrix}\begin{pmatrix}r\\s\\t\\u\end{pmatrix}$$

 

[Leanna]

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. )

 

[MarkFL]

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:

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

 

[Leanna]

Thanks a lot