Linear Algebra Question

[tautis154]

Hello, I am stuck on the assignment and I am not sure how I should do it. Would I be correct in saying that u1 = (1;1;2) u2 = (2;-1;2) u3 = (1;2;3)

 

[HallsofIvy]

That's awkwardly worded! \(\displaystyle u_1\), \(\displaystyle u_2\), and \(\displaystyle u_3\) have already been defined! I think it means to write \(\displaystyle Eu_1\), \(\displaystyle Eu_2\), and \(\displaystyle Eu_3\) in terms of \(\displaystyle e_1\), \(\displaystyle e_2\) and \(\displaystyle e_3\). And since they are the "standard basis" it really just means to do the matrix multiplications \(\displaystyle P_{S\to E}u_1\), \(\displaystyle P_{S\to E}u_2\), and \(\displaystyle P_{S\to E}u_3\);

So what is \(\displaystyle \begin{bmatrix}1 & 2 & 1 \\ 1 & -1 & 2 \\ 2 & 2 & 3\end{bmatrix}\begin{bmatrix}1\\ 1 \\ 2 \end{bmatrix}\)?

What is \(\displaystyle \begin{bmatrix}1 & 2 & 1 \\ 1 & -1 & 2 \\ 2 & 2 & 3\end{bmatrix}\begin{bmatrix}2\\ -1 \\ 2 \end{bmatrix}\)?

What is \(\displaystyle \begin{bmatrix}1 & 2 & 1 \\ 1 & -1 & 2 \\ 2 & 2 & 3\end{bmatrix}\begin{bmatrix}1\\ 2 \\ 3 \end{bmatrix}\)?

 

[tautis154]

Thanks a lot could I ask you about my other problems too?

 

[Steven G]

Just make another post for that other question.