Exercise 1.1.8

Question

$\boldsymbol{A}=\boldsymbol{C R}$ is a representation of the columns of $A$ in the basis formed by the columns of $C$ with coefficients in $R$. If $A_{i j}=j^{2}$ is 3 by 3 , write down $A$ and $C$ and $R$.

Neil Z. · Accepted Answer

Since $A_{ij}=j^2$, so we have $$A=\begin{bmatrix}1&4&9\1&4&9\1&4&9\end{bmatrix},$$ we see that $$C=\begin{bmatrix}1\1\1\end{bmatrix},$$ because the other two columns are just multiplier of this one. It's easy to see that $$R=\begin{bmatrix}1 & 4 & 9\end{bmatrix}.$$

Exercise 1.1.8

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Exercise 1.1.8

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