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.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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?
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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