- #1
leeewl
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Hi I'm stuck on this problem and I could not find similar examples anywhere.. any help would be greatly appreciated, thank you.
Compute the change of basis matrix that takes the basis
[itex]V1 = \begin{bmatrix} -1 \\ 3 \end{bmatrix}[/itex] [itex]V2 = \begin{bmatrix} 2 \\ 5 \end{bmatrix}[/itex]
of R2 to the basis
[itex]W1 = \begin{bmatrix} 2 \\ 5 \end{bmatrix}[/itex] [itex]W2 = \begin{bmatrix} 3 \\ 7 \end{bmatrix}[/itex]
I have done this first part, the change of basis matrix is [itex]A = \begin{bmatrix} 2 & 1 \\ -1 & 0 \end{bmatrix}[/itex]
next part I don't quite know how to start:
Consider v = V1 + 2(V2) [itex]\in[/itex] R2: Determine the column vector [itex]\begin{bmatrix} a \\ b \end{bmatrix}[/itex] which represents v with respect to the basis {W1, W2}
Do I turn v1 into [itex]V1 = \begin{bmatrix} -1 \\ 3 \end{bmatrix}[/itex] and V2 into [itex]V2 = \begin{bmatrix} 4 \\ 10 \end{bmatrix}[/itex] and then try and find a linear combination that gives me {W1, W2}?
Homework Statement
Compute the change of basis matrix that takes the basis
[itex]V1 = \begin{bmatrix} -1 \\ 3 \end{bmatrix}[/itex] [itex]V2 = \begin{bmatrix} 2 \\ 5 \end{bmatrix}[/itex]
of R2 to the basis
[itex]W1 = \begin{bmatrix} 2 \\ 5 \end{bmatrix}[/itex] [itex]W2 = \begin{bmatrix} 3 \\ 7 \end{bmatrix}[/itex]
I have done this first part, the change of basis matrix is [itex]A = \begin{bmatrix} 2 & 1 \\ -1 & 0 \end{bmatrix}[/itex]
next part I don't quite know how to start:
Consider v = V1 + 2(V2) [itex]\in[/itex] R2: Determine the column vector [itex]\begin{bmatrix} a \\ b \end{bmatrix}[/itex] which represents v with respect to the basis {W1, W2}
The Attempt at a Solution
Do I turn v1 into [itex]V1 = \begin{bmatrix} -1 \\ 3 \end{bmatrix}[/itex] and V2 into [itex]V2 = \begin{bmatrix} 4 \\ 10 \end{bmatrix}[/itex] and then try and find a linear combination that gives me {W1, W2}?