Suppose S: R² → R² and T: R² → R² are linear transformations given by s([])-|z]+()-|zx (a) Find the standard matrix for S (assuming the stand basis for R³ and for R²). (b) Find the standard matrix for T (assuming the standard basis for R² and for R³). (c) Show that S and T are invertible.
Suppose S: R² → R² and T: R² → R² are linear transformations given by s([])-|z]+()-|zx (a) Find the standard matrix for S (assuming the stand basis for R³ and for R²). (b) Find the standard matrix for T (assuming the standard basis for R² and for R³). (c) Show that S and T are invertible.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.6: Introduction To Linear Transformations
Problem 55EQ
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![Suppose S: R² → R² and T: R² → R² are linear
transformations given by
3x y
(0)-[-1-(C)-[22]
T
-x-3y]
(a) Find the standard matrix for S (assuming the stand basis for R³
and for R²).
(b) Find the standard matrix for T (assuming the standard basis for R²
and for R³).
(c) Show that S and T are invertible.
(d) Show that T is the inverse of S.
(e) What is the standard matrix for T(S(z)) = To S(1), where I = R²?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F39ee3059-6733-456c-bbc4-46bedd3c18f2%2Fe2ef4286-9ff7-4a10-81e8-74fef5be92d5%2Fi79vo7b_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose S: R² → R² and T: R² → R² are linear
transformations given by
3x y
(0)-[-1-(C)-[22]
T
-x-3y]
(a) Find the standard matrix for S (assuming the stand basis for R³
and for R²).
(b) Find the standard matrix for T (assuming the standard basis for R²
and for R³).
(c) Show that S and T are invertible.
(d) Show that T is the inverse of S.
(e) What is the standard matrix for T(S(z)) = To S(1), where I = R²?
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