Question 19 - Week 4 Practice

Question 19

00:00Est. 2 min

Marks:+2.000.00

Passage

Consider the following subspaces of

M_{2\times2}(\mathbb{R})

with the usual addition and scalar multiplication:

W_1=\left\{\begin{bmatrix}a&b\\c&d\end{bmatrix}\mid a+d=0\right\},\quad W_2=\left\{\begin{bmatrix}a&b\\c&d\end{bmatrix}\mid a+b=0,\ c+d=0\right\}.

Now consider the matrices

B_1=\begin{bmatrix}1&0\\0&0\end{bmatrix}

B_2=\begin{bmatrix}0&1\\0&0\end{bmatrix}

B_3=\begin{bmatrix}0&0\\1&0\end{bmatrix}

B_4=\begin{bmatrix}0&0\\0&1\end{bmatrix}

B_5=\begin{bmatrix}1&0\\0&-1\end{bmatrix}

B_6=\begin{bmatrix}1&-1\\0&0\end{bmatrix}

, and

B_7=\begin{bmatrix}0&0\\1&-1\end{bmatrix}

. Based on the above data, answer the given subquestions.

Question

Choose the correct set of matrices that forms a basis for

W_1

Comprehension

Medium Difficulty

23 February 2025