Questions askedCategory: 2568pg. 239 #21
nlamantia asked 8 months ago

The book said to use equation 6, but I don’t know how it applies.  When I tried to apply equation 6, I kept getting the wrong answer.  Could you please walk me through this problem?  Thanks!


1 Answers
Best Answer
TheYoYoMaster answered 8 months ago

Use the fact that:
\[\begin{bmatrix}
1 \\
0
\end{bmatrix}=\frac{1}{2}\left(\,\begin{bmatrix}
1 \\
1
\end{bmatrix}+\begin{bmatrix}
1 \\
-1
\end{bmatrix}\,\right)\] \[\begin{bmatrix}
0 \\
1
\end{bmatrix}=\frac{1}{2}\left(\,\begin{bmatrix}
1 \\
1
\end{bmatrix}-\begin{bmatrix}
1 \\
-1
\end{bmatrix}\,\right).\] Find $T\left(\, \begin{bmatrix}
1 \\
0
\end{bmatrix} \,\right)$ and $T\left(\, \begin{bmatrix}
0 \\
1
\end{bmatrix} \,\right)$ and write $T\left(\, \begin{bmatrix}
x_1 \\
x_2
\end{bmatrix} \,\right)$ as a linear combination of these two.
Hope that helps!
Different methods to solve this kind of problems are explained in Find a general formula of a linear transformation from $\R^2$ to $\R^3$


nlamantia replied 8 months ago

Thank you! That makes sense!