Question
Verify that $W$ is a subspace of $V$. In each case, assume that $V$ has the standard operations.$W$ is the set of all $3 \times 2$ matrices of the form$\left[\begin{array}{rrr}a & b \\ a-2 b & 0 \\ 0 & c\end{array}\right]$$V=M_{3,2}$
Step 1
Let's take two matrices $A$ and $B$ from the set $W$. $A = \left[\begin{array}{rrr}a_1 & b_1 \\ a_1-2 b_1 & 0 \\ 0 & c_1\end{array}\right]$ and $B = \left[\begin{array}{rrr}a_2 & b_2 \\ a_2-2 b_2 & 0 \\ 0 & c_2\end{array}\right]$ If we add these two matrices, we Show more…
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