In Exercise 7, do the parts of Exercise 1 for the given linear transformation, bases, and vector v.Please solve question #7, ONLY question #7. PLEASE write it on PAPER. 1. Let T: R² → R2 be the linear transformation+ x₂[3]-[***]TX2a) Find [7] where a is the standard basis for R².b) Let 6 be the basis consisting of1[3][7]-1for R2. Find the change of basis matrix from ato B.c) Find the change of basis matrix from ß to a.d) Find [7].e) Find [v]s forV=<-2f) Find [T(v)].g) Use the result of part (f) to find T (v). 7. D: V→ V where V is the set of solutions to thedifferential equation y" + y = 0; a the basis of Vconsisting of sin x, cos x; ß the basis consisting ofsin x + cos x, sin x - cos x; v = 3 cos x - 2 sin x.

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1. Let T: R² → R2 be the linear transformation T[*]-[***] a) Find [T] where a is the standard basis for R². b) Let 6 be the basis consisting of X2 x2 -2 [3][7] for R2. Find the change of basis matrix from a to ß. c) Find the change of basis matrix from ß to a. d) Find [7]. e) Find [v]s for v=[²3] · f) Find [T(v)]. g) Use the result of part (f) to find T (v).

1. Let T: R² → R2 be the linear transformation T[*]-[***] a) Find [T] where a is the standard basis for R². b) Let 6 be the basis consisting of X2 x2 -2 [3][7] for R2. Find the change of basis matrix from a to ß. c) Find the change of basis matrix from ß to a. d) Find [7]. e) Find [v]s for v=[²3] · f) Find [T(v)]. g) Use the result of part (f) to find T (v).

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

In Exercise 7, do the parts of Exercise 1 for the given linear transformation, bases, and vector v.

Please solve question #7, ONLY question #7. PLEASE write it on PAPER.

1. Let T: R² → R2 be the linear transformation
+ x₂
[3]-[***]
T
X2
a) Find [7] where a is the standard basis for R².
b) Let 6 be the basis consisting of
1
[3][7]
-1
for R2. Find the change of basis matrix from a
to B.
c) Find the change of basis matrix from ß to a.
d) Find [7].
e) Find [v]s for
V=
<-2
f) Find [T(v)].
g) Use the result of part (f) to find T (v).

7. D: V→ V where V is the set of solutions to the
differential equation y" + y = 0; a the basis of V
consisting of sin x, cos x; ß the basis consisting of
sin x + cos x, sin x - cos x; v = 3 cos x - 2 sin x.

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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