х-у х- у+22 2х - Зу+z Let T у x+2y |. Find the matrix for each transformation, y 2х - 4y and for the composition T o S.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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[Matrix Transformations] How do you solve this?

x- y
х- у+22
Let T
Find the matrix for each transformation,
x+2y
2х - 4y
y
2х - Зу+z
and for the composition To S.
Transcribed Image Text:x- y х- у+22 Let T Find the matrix for each transformation, x+2y 2х - 4y y 2х - Зу+z and for the composition To S.
Operations on Transformations
Recall: If f : A → B, g : B → C, then we can compose f, g to get a function gof: A→ C given by
(go f)(x) = g(f(x)).
If A is m x k, B is k × n, then AB is m × n, and hence defines a transformation TAB : R"
Rm.
The following theorem connects TẠ, TB, TAB.
Theorem 2
Suppose that A is m x k and B is k × n. Then TAB = TAO Tg.
I.e. matrix multiplication corresponds to composition of matrix transformations.
Transcribed Image Text:Operations on Transformations Recall: If f : A → B, g : B → C, then we can compose f, g to get a function gof: A→ C given by (go f)(x) = g(f(x)). If A is m x k, B is k × n, then AB is m × n, and hence defines a transformation TAB : R" Rm. The following theorem connects TẠ, TB, TAB. Theorem 2 Suppose that A is m x k and B is k × n. Then TAB = TAO Tg. I.e. matrix multiplication corresponds to composition of matrix transformations.
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