Question

Could someone check my working for me, please? I will give the question in the comments, as it contains matrices, etc :)

Answer 1

For the ordered basis \[B = \left\{ \left[\begin{matrix}0 & 1 \\ 1 & 1\end{matrix}\right], \left[\begin{matrix}1 & 0 \\ 1 & 1\end{matrix}\right], \left[\begin{matrix}1 & 1 \\ 0 & 1\end{matrix}\right], \left[\begin{matrix}1 & 1 \\ 1 & 0\end{matrix}\right] \right\}\] find the coordinate vector \[\left[\begin{matrix}6 & 3 \\ 7 & 2\end{matrix}\right]\] with respect to B.

Answer 2

I have attempted to solve this by putting the given matrices, in vector form, into the matrix \[\left[\begin{matrix}1 & 0 &1&1 |& 3\\ 0 & 1&1&1|&6\\1&1&0&1|&7\\1&1&1&0|&2\end{matrix}\right]\]
getting a reduced matrix \[\left[\begin{matrix}1 & 0 &1&1 |& 3\\ 0 & 1&1&1|&6\\0&0&-2&-1|&-2\\0&0&0&-3/2|&-6\end{matrix}\right]\] solving the system gets c_1 = 0; c_2 = 3; c_3 = -1; c_4 = 4
Therefore the coordinate vector is\[x_B = \left(\begin{matrix}0 \\ 3\\-1\\4\end{matrix}\right)\]

Answer 3

that look correct to me! nice job :)

Answer 4

Cheers!