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In Exercises 1–10, assume that T is a linear
Chapter 1, Problem 10E(choose chapter or problem)
In Exercises 1–10, assume that T is a linear transformation. Find the standard matrix of T.
\(T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{4}, T\left(\mathbf{e}_{1}\right)=(3,1,3,1) \text { and } T\left(\mathbf{e}_{2}\right)=(-5,2,0,0)\), where \(\mathbf{e}_{1}=(1,0) \text { and } \mathbf{e}_{2}=(0,1)\)
Questions & Answers
QUESTION:
In Exercises 1–10, assume that T is a linear transformation. Find the standard matrix of T.
\(T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{4}, T\left(\mathbf{e}_{1}\right)=(3,1,3,1) \text { and } T\left(\mathbf{e}_{2}\right)=(-5,2,0,0)\), where \(\mathbf{e}_{1}=(1,0) \text { and } \mathbf{e}_{2}=(0,1)\)
ANSWER:Solution:-
Step1
Given that
Assume that T is a linear transformation.T : ℝ2 → ℝ2 first reflects points through the horizontal x1-axis and then rotates points –π/2 radians.
Step2