Exercise 1.1.10

Question

Find the matrices $C_{1}$ and $C_{2}$ containing independent columns of $A_{1}$ and $A_{2}$ :
$$
A_{1}=\left[\begin{array}{lll}
1 & 3 & -2 \
3 & 9 & -6 \
2 & 6 & -4
\end{array}ight] \quad A_{2}=\left[\begin{array}{lll}
1 & 2 & 3 \
4 & 5 & 6 \
7 & 8 & 9
\end{array}ight].
$$

Neil Z. · Accepted Answer

\begin{itemize}
\item For $A_1$, we have $$C_1=\begin{bmatrix}1 \ 3 \ 2\end{bmatrix}$$ because the other two columns are multiple of the first column. 
\item For $A_2$, we have $$C_2= \begin{bmatrix}1 & 2\ 4 &5\ 7 & 8\end{bmatrix}$$ because the third column is $-1$ multiply first column plus 2 multiply the second column.
\end{itemize}

Exercise 1.1.10

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Exercise 1.1.10

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