Khan exercises Maths Tools 1
Given v=(85−4) v = \begin{pmatrix}8 \\ 5 \\ -4 \end{pmatrix} v=85−4 and a basis B={(200),(0−31),(0−2−6)}\mathcal B = \left\{ \begin{pmatrix} 2 \\ 0\\ 0\end{pmatrix}, \begin{pmatrix} 0 \\ -3\\ 1\end{pmatrix}, \begin{pmatrix} 0 \\ -2\\ -6\end{pmatrix} \right\}B=⎩⎨⎧200,0−31,0−2−6⎭⎬⎫.
v=(85−4) v = \begin{pmatrix}8 \\ 5 \\ -4 \end{pmatrix} v=85−4
B={(200),(0−31),(0−2−6)}\mathcal B = \left\{ \begin{pmatrix} 2 \\ 0\\ 0\end{pmatrix}, \begin{pmatrix} 0 \\ -3\\ 1\end{pmatrix}, \begin{pmatrix} 0 \\ -2\\ -6\end{pmatrix} \right\}B=⎩⎨⎧200,0−31,0−2−6⎭⎬⎫
Calculate the coordinate vector [v]B=(XYZ)[v]_{\mathcal B} = \begin{pmatrix} {\color{red}X} \\ {\color{blue}Y} \\ Z \end{pmatrix}[v]B=XYZ of vvv with respect to the basis B\mathcal B B.
[v]B=(XYZ)[v]_{\mathcal B} = \begin{pmatrix} {\color{red}X} \\ {\color{blue}Y} \\ Z \end{pmatrix}[v]B=XYZ
vvv
B\mathcal B B
X=\color{red} X =X=
Y=\color{blue} Y =Y=
Z=Z =Z=