Question 4. Let L: R → R be a linear transformation in the Euclidean space defined by L(¤1, x2) = (5x1 + 2x2, –3x1 + 2x2)". (a) Find the matrix [L]ST relative to the bases S = {(1,2)", (1, –1)"} and T = {(1,0), (1, 1)} (b) Find the coordinate vectors [(3, 4)"]s, [L(3, 4)]T and then use [L]sT to find L(3, 4). Verify the last result by computing L(3, 4) directly.
Question 4. Let L: R → R be a linear transformation in the Euclidean space defined by L(¤1, x2) = (5x1 + 2x2, –3x1 + 2x2)". (a) Find the matrix [L]ST relative to the bases S = {(1,2)", (1, –1)"} and T = {(1,0), (1, 1)} (b) Find the coordinate vectors [(3, 4)"]s, [L(3, 4)]T and then use [L]sT to find L(3, 4). Verify the last result by computing L(3, 4) directly.
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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![Question 4. Let L: R → R be a linear transformation in the Euclidean space defined by
L(x1, x2)
= (5x1 + 2x2, -3.x1+ 2x2)".
(a) Find the matrix [L]ST relative to the bases S = {(1, 2)", (1,–1)"} andT
{(1,0), (1, 1)}
(b) Find the coordinate vectors [(3, 4)"]s, [L(3, 4)]r and then use [L]sT to find L(3,4). Verify
the last result by computing L(3, 4) directly.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F80bf294b-e7db-4543-8681-94647e123fff%2F488d2c54-f651-41f0-8146-0841b5ab2f29%2Fip24of2_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 4. Let L: R → R be a linear transformation in the Euclidean space defined by
L(x1, x2)
= (5x1 + 2x2, -3.x1+ 2x2)".
(a) Find the matrix [L]ST relative to the bases S = {(1, 2)", (1,–1)"} andT
{(1,0), (1, 1)}
(b) Find the coordinate vectors [(3, 4)"]s, [L(3, 4)]r and then use [L]sT to find L(3,4). Verify
the last result by computing L(3, 4) directly.
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