Answer
Rows of AB are linearly dependent
Work Step by Step
\[
\text { put } A=\left[\begin{array}{l}
a_{1} \\
a_{2} \\
a_{n}
\end{array}\right]
\]
1) Because. the rows' of A are.linearly dependent
\[
C_{1} a_{1}+c_{2} a_{2}+\dots+c_{n} a_{n}=0
\]
2) After matrix multiplication,
\[
A B=\left[\begin{array}{c}
a_{1} B \\
a_{2} B \\
\vdots \\
a_{n} B
\end{array}\right]
\]
where the rows of $A B$ are
given by rows of $A^{\prime}$ multiplied.
by $^{\prime} B^{\prime}$
To prove that $\quad$ rows of $A B$ are
linear dependent assume the Statement is trace.
trace is so rows of $A B$ are linearly dependent.
