QUESTION 2 for Gradescope: (a) Use the Marquis de LaPlace (a…

QUESTION 2 for Gradescope: (a) Use the Marquis de LaPlace (aka Gram-Schmidt) process to find an orthogonal basis with the same span as { , } {“version”:”1.1″,”math”:”\left\{ \begin{bmatrix} 2 \\ 4\\ 2 \end{bmatrix}, \begin{bmatrix} 2 \\ 1 \\-1\end{bmatrix} \right\}”} Note that your orthogonal basis does not need to be orthonormal. (b) Use the orthogonal basis found in part (a) to find the least squares solution to the following problem. Do not use a method to find the least squares solution that was not covered in the lectures. {2x+2y=04x+y=−22x−y=1{“version”:”1.1″,”math”:”\begin{cases} 2x+2y & =0 \\ 4x+y & = -2 \\ 2x-y & = 1 \end{cases}”}

QUESTION 6(a) for Gradescope: If  u  and  v {“version”:”1.1″…

QUESTION 6(a) for Gradescope: If  u  and  v {“version”:”1.1″,”math”:”u \text{ and } v”} are non-zero vectors in n-space, then  span { u , v } {“version”:”1.1″,”math”:”\text{span}\{u,v\}”}does NOT contain the zero vector.