Question 5 Let T: R² R² be the reflection through the x-axis. a) Find the standard matrix of T. b) Show that T is an isomorphism and find a formula for T-¹. c) Consider the basis {(1,2), (1,0)) of R². Find the matrix of T relative to this basis.

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Chapter2: Second-order Linear Odes
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Question 5
Let T: R² R² be the reflection through the x-axis.
a) Find the standard matrix of T.
b) Show that T is an isomorphism and find a formula for T-¹.
c) Consider the basis {(1,2), (1,0)) of R². Find the matrix of T relative to this basis.
Transcribed Image Text:Question 5 Let T: R² R² be the reflection through the x-axis. a) Find the standard matrix of T. b) Show that T is an isomorphism and find a formula for T-¹. c) Consider the basis {(1,2), (1,0)) of R². Find the matrix of T relative to this basis.
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