Consider the sets of vectors: A = (3,6,30),(9,15,81),(-2, – 8, – 34)}. |B = {(- 1, – 5, – 24),(-4, – 19, – 91),(-6, – 24, – 111)}, Witch form two bases of R3! 40 9 a) Calculate the coordinates in the canonical base of Rof the vector V = ( 3 ,3, 2 )A expressed in base A b) Calculate the coordinates of the vector V = (-4,1, –- 4) at bases A and B. c) Calculate the base change matrix from B to A d) Consider the vector w given by the coordinates W = (-3,2, – 4), at base B. Calculate the coordinates of this vector at base A. e) Let C be a new base of R3. If the base change matrix, from base A to base C is - 10 55 32 35 -5 3 -5 25 21 calculate the coordinates of the vector v in section 1 on the base C.
Consider the sets of vectors: A = (3,6,30),(9,15,81),(-2, – 8, – 34)}. |B = {(- 1, – 5, – 24),(-4, – 19, – 91),(-6, – 24, – 111)}, Witch form two bases of R3! 40 9 a) Calculate the coordinates in the canonical base of Rof the vector V = ( 3 ,3, 2 )A expressed in base A b) Calculate the coordinates of the vector V = (-4,1, –- 4) at bases A and B. c) Calculate the base change matrix from B to A d) Consider the vector w given by the coordinates W = (-3,2, – 4), at base B. Calculate the coordinates of this vector at base A. e) Let C be a new base of R3. If the base change matrix, from base A to base C is - 10 55 32 35 -5 3 -5 25 21 calculate the coordinates of the vector v in section 1 on the base C.
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
plz provide handwritten answer for part d
Transcribed Image Text:1.
Consider the sets of vectors:
A = {(3,6,30),(9,15,81),(-2, – 8, - 34)},
B = {(-1,– 5, – 24),(-4, – 19, – 91),(-6, – 24, – 111)},
Witch form two bases of R.
40
9
- -
- -
a) Calculate the coordinates in the canonical base of R°of the vector V = ( 3 ,3, 2 JA
expressed in base A
b) Calculate the coordinates of the vector V = (-4,1, – 4) at bases A and B.
c) Calculate the base change matrix from B to A
d) Consider the vector w given by the coordinates W = (-3,2, – 4), at base B. Calculate the
coordinates of this vector at base A.
e) Let C be a new base of R3. If the base change matrix, from base A to base Cis
- 10
55 32
35
-5
3
- -
-5
25
21
calculate the coordinates of the vector v in section 1 on the base C.
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