QUESTION 3 for Gradescope: Consider the linear transformatio…

QUESTION 3 for Gradescope: Consider the linear transformation with matrix representation A=[21430−1].{“version”:”1.1″,”math”:”A=\begin{bmatrix} 2 & 1 & 4 \\ 3 & 0 & -1 \end{bmatrix}.”} Find an intrinsic description of the kernel of this linear transformation. Show all your work. State the nullity and rank of A based on your work for finding the kernel.

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 { [ 2 4 2 ] , [ 2 1 − 1 ] } {“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}”}