Linear Algebra Question

[Guest]

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]

Didn't we seen this before?

Let [tex]u= (a, b, c)[/tex] Then [tex]Pu= \begin{bmatrix}1 & 2 & 1 \\ 1 & -1 & 2 \\ 2 & 2 & 3 \end{bmatrix}\begin{bmatrix}a \\ b \\ c \end{bmatrix}= \begin{bmatrix}a+ 2b+ c \\ a- b+ 2c \\ 2a+ 2b+ 3c\end{bmatrix}[/tex]. We are told that [tex]Pu= \begin{bmatrix}1 \\ 0 \\ 0 \end{bmatrix}[/tex].

So we have the three equations a+ 2b+ c= 1, a- b+ c= 0, and 2a+ 2b+ 3c= 0. Solve those equations for a, b, and c. Do the same for v and w.

[HallsofIvy]

Ouch! "Didn't we seen" should have been either "Didn't we see" or "Haven't we seen". I lost track of what I was writing!