1 (a) For each of the following transformations f: R2 → R2, say whether f is linear or not. (i) f(x, y) = (0, y-3x) (ii) f(x, y) = (x-y-1,2x+y) (iii) f(x, y) = (x, y) = If it is, write down the matrix that represents f relative to the standard basis {i,j}. (b) Let f and g be linear transformations represented by the matrices A = [23] and B respectively, relative to the standard basis {i, j}. Determine the matrices that represent the composite transformations [33], 4 (i) gof: R² R² (ii) fog: R2 R² Hence find a rule for each composite transformation in the form F(x, y) = (ax + by, cx + dy).
1 (a) For each of the following transformations f: R2 → R2, say whether f is linear or not. (i) f(x, y) = (0, y-3x) (ii) f(x, y) = (x-y-1,2x+y) (iii) f(x, y) = (x, y) = If it is, write down the matrix that represents f relative to the standard basis {i,j}. (b) Let f and g be linear transformations represented by the matrices A = [23] and B respectively, relative to the standard basis {i, j}. Determine the matrices that represent the composite transformations [33], 4 (i) gof: R² R² (ii) fog: R2 R² Hence find a rule for each composite transformation in the form F(x, y) = (ax + by, cx + dy).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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solve for 1b， thanks
![1 (a) For each of the following transformations f: R² → R², say whether f is linear or not.
(i) f(x, y) = (0, y-3x)
(ii) f(x, y) = (x−y—1,2x+y) (iii) f(x, y) = (x, y)
-2
If it is, write down the matrix that represents f relative to the standard basis {i,j}.
(b) Let f and g be linear transformations represented by the matrices A [²3] and B =
4-3]
respectively, relative to the standard basis {i, j}. Determine the matrices that represent the composite
transformations
=
[33],
(i) gof: R² → R²
(ii) fog: R2 R²
Hence find a rule for each composite transformation in the form F(x, y) = (ax + by, cx + dy).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff1ea36b0-99c2-47c7-ac0a-6ed7dd463e6c%2Fd6adbd66-d1df-4b65-a323-15b89739a81a%2Feb3o6u_processed.png&w=3840&q=75)
Transcribed Image Text:1 (a) For each of the following transformations f: R² → R², say whether f is linear or not.
(i) f(x, y) = (0, y-3x)
(ii) f(x, y) = (x−y—1,2x+y) (iii) f(x, y) = (x, y)
-2
If it is, write down the matrix that represents f relative to the standard basis {i,j}.
(b) Let f and g be linear transformations represented by the matrices A [²3] and B =
4-3]
respectively, relative to the standard basis {i, j}. Determine the matrices that represent the composite
transformations
=
[33],
(i) gof: R² → R²
(ii) fog: R2 R²
Hence find a rule for each composite transformation in the form F(x, y) = (ax + by, cx + dy).
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