2 15 7 4 9 2 1 5 7 4 9 1 Let A = (place your whole ID in each row) Calculations. 1. Define a linear transformation T: R® → R² by T(x) = Ax. a) Calculate the image of (1, 0, 2, 1, 2, -1, 1, 2). b) Calculate the pre-image of (60, 120). c) Determine a basis of the range of the transformation.

2 15 7 4 9 2 1 5 7 4 9 1 Let A = (place your whole ID in each row) Calculations. 1. Define a linear transformation T: R® → R² by T(x) = Ax. a) Calculate the image of (1, 0, 2, 1, 2, -1, 1, 2). b) Calculate the pre-image of (60, 120). c) Determine a basis of the range of the transformation.

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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MAT280 Fall2020 TakeHome 119 update (1) - Word
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[5
6.
Let å = 2 (first two ID digits), b = 7 (middle three ID digits), c 1 (1last two digits)
Let u =
(first three digits), v =
(last four digits)
1
Let A =
2 1 5 7 4 9
5 7 4
(place your whole ID in each row)
1
9.
Calculations.
1. Define a linear transformation T: R → R² by T(x) = Ax.
a) Calculate the image of (1, 0, 2, 1, 2, -1, 1, 2).
b) Calculate the pre-image of (60, 120).
c) Determine a basis of the range of the transformation.
d) Determine a basis for the kernel of the transformation.
2. Define T: R → R° such that T(a) = (1,2,1), T(b) = (0,1,3), T(2) = (1,0, –1).
Calculate T(-2,3, – 1).
3. Define T: R? → R² by T(x, y) = (3x – 2y, y - 2x).
a) Construct the standard matrix for T.
b) Construct the matrix for T relative to the basis {(5,2), (2,1)}.
c) Construct the matrix for T-1 relative to the basis {(1,1), (1,2)}.
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