[All Steps] Are the following subspaces of the 2 * 2 matrices? Justify your answer. The matrices [lla b , c d] with a+b+c+d=0. The matrices of the form

Question: Are the following subspaces of the $2 \times 2$ matrices? Justify your answer.

The matrices $\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]$ with $a+b+c+d=0$.
The matrices of the form $\left[\begin{array}{rr}a & 0 \\ -a & 0\end{array}\right]$
The $2 \times 2$ matrices $A$ with $\operatorname{det} A=0$.
The $1 \times 2$ matrices.

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[All Steps] Are the following subspaces of the 2 * 2 matrices? Justify your answer. The matrices [lla b , c d] with a+b+c+d=0. The matrices of the form

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