Answer by Arthur for Linear Transformation and Basis
In the standard basis $\mathcal S$, we have $T$ represented by$$[T]_{\mathcal S} = \begin{bmatrix}-2&-5\\2&4\end{bmatrix}$$Now we need to find some invertible matrix $B$ such that $B^{-1}T_SB$...
View ArticleAnswer by José Carlos Santos for Linear Transformation and Basis
The matrix of $T$ with respect to the canonical basis is $\left[\begin{smallmatrix}-2&-5\\2&4\end{smallmatrix}\right]$, whose trace is $2$ and whose determinant is also $2$. So, if your problem...
View ArticleAnswer by user for Linear Transformation and Basis
We have that the matrix from basis $B$ to canonical is$$u_C=M_Bu_B$$then$$T_C(u)=\left[\begin{array}{cc}{-2} & {-5} \\ {2} & {4}\end{array}\right]u_C=\left[\begin{array}{cc}{-2} & {-5} \\...
View ArticleLinear Transformation and Basis
$$\begin{array}{l}{\text { 2.) Consider the linear transformation } T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2},\left[\begin{array}{l}{x} \\ {y}\end{array}\right] \mapsto\left[\begin{array}{c}{-2 x-5...
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