Exercise 1.1.12

Question

Produce a basis for the column spaces of $A_{1}$ and $A_{2}$. What are the dimensions of those column spaces-the number of independent vectors? What are the ranks of $A_{1}$ and $A_{2}$? How many independent rows in $A_{1}$ and $A_{2}$?

Neil Z. · Accepted Answer

\begin{itemize}
\item
  The basis for $A_1$ are columns in $C_1$ and the basis for $A_2$
  are columns in $C_2$.
\item
  The dimension of column space for $A_1$ is 1, for $A_2$ is 2.
\item
  The rank of $A_1$ is 1, for $A_2$ is 2.
\item
  There are 1 independent row in $A_1$, and 2 independent rows in
  $A_2$.
\end{itemize}

Exercise 1.1.12

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Exercise 1.1.12

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