- #1
raay
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Hi can anyone give me some hints with this question thanks
A = \begin{pmatrix} 3 & -2 &1 & 0 \\ 1 & 6 & 2 & 1 \\ -3 & 0 & 7 & 1 \end{pmatrix}
be a matrix for T:ℝ4→ℝ3 relative to the basis
B = {v1, v2, v3, v4} and B'= {w1, w2, w3}
v1 = \begin{pmatrix} 0 \\ 1 \\ 1 \\ 1 \end{pmatrix}
v2 = \begin{pmatrix} 2 \\ 1 \\ -1 \\ -1 \end{pmatrix}
v3 = \begin{pmatrix} 1 \\ 4 \\ -1 \\ 2 \end{pmatrix}
v4 = \begin{pmatrix} 6 \\ 9 \\ 4 \\ 2 \end{pmatrix}
w1 = \begin{pmatrix} 0 \\ 8 \\ 8 \end{pmatrix}
w2 = \begin{pmatrix} -7 \\ 8 \\ -1 \end{pmatrix}
w3 = \begin{pmatrix} -6 \\ 9 \\ 1 \end{pmatrix}
a- Find [T(v_1)]B' , [T(v_2)]B' , [T(v_3)]B' and [T(v_4)]B'.
b- Find T(v1), T(v2), T(v3) and T(v4).
c- Find a formula for T( \begin{pmatrix} x_1 \\ x_2 \\ x_3 \\ x_4 \end{pmatrix} )
Attempt solution for part (a)
[T(v)]B' = [T]B→B' × [v]B
If this is right I don't know how to use it.
Also i tried drawing a diagram but i think i have to use the diagram to find a formula for T in part (c).
Thanks
A = \begin{pmatrix} 3 & -2 &1 & 0 \\ 1 & 6 & 2 & 1 \\ -3 & 0 & 7 & 1 \end{pmatrix}
be a matrix for T:ℝ4→ℝ3 relative to the basis
B = {v1, v2, v3, v4} and B'= {w1, w2, w3}
v1 = \begin{pmatrix} 0 \\ 1 \\ 1 \\ 1 \end{pmatrix}
v2 = \begin{pmatrix} 2 \\ 1 \\ -1 \\ -1 \end{pmatrix}
v3 = \begin{pmatrix} 1 \\ 4 \\ -1 \\ 2 \end{pmatrix}
v4 = \begin{pmatrix} 6 \\ 9 \\ 4 \\ 2 \end{pmatrix}
w1 = \begin{pmatrix} 0 \\ 8 \\ 8 \end{pmatrix}
w2 = \begin{pmatrix} -7 \\ 8 \\ -1 \end{pmatrix}
w3 = \begin{pmatrix} -6 \\ 9 \\ 1 \end{pmatrix}
a- Find [T(v_1)]B' , [T(v_2)]B' , [T(v_3)]B' and [T(v_4)]B'.
b- Find T(v1), T(v2), T(v3) and T(v4).
c- Find a formula for T( \begin{pmatrix} x_1 \\ x_2 \\ x_3 \\ x_4 \end{pmatrix} )
Attempt solution for part (a)
[T(v)]B' = [T]B→B' × [v]B
If this is right I don't know how to use it.
Also i tried drawing a diagram but i think i have to use the diagram to find a formula for T in part (c).
Thanks
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