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Let B = {(1, 1, 0), (0, 1, 1), (1, 0, 1)) and B' = {(1, 0, 0), (0, 1, 0), (0, 0, 1)) be bases for R", and let N/A N/WN/H P= be the matrix for T: R³ R³ relative to B. -1 (a) Find the transition matrix P from B to B. 633 11 [v]a (b) Use the matrices P and A to find [v] and [7(v)], where [v]=[-1 1 0]. N/A N/N/G₂ [T(v)]=3 p-1 = 0 0 -1 (c) Find P¹ and A' (the matrix for 7 relative to B¹). 0 4/3 A'= 3/2 1/2 -2 -1 b (d) Find [7(v)] two ways. [T(V)] = P¹[T(V)] = 3 0 0 1 3/2 E [T(v)]=A[v]=3 -1/2 E =

Let B = {(1, 1, 0), (0, 1, 1), (1, 0, 1)) and B' = {(1, 0, 0), (0, 1, 0), (0, 0, 1)) be bases for R", and let N/A N/WN/H P= be the matrix for T: R³ R³ relative to B. -1 (a) Find the transition matrix P from B to B. 633 11 [v]a (b) Use the matrices P and A to find [v] and [7(v)], where [v]=[-1 1 0]. N/A N/N/G₂ [T(v)]=3 p-1 = 0 0 -1 (c) Find P¹ and A' (the matrix for 7 relative to B¹). 0 4/3 A'= 3/2 1/2 -2 -1 b (d) Find [7(v)] two ways. [T(V)] = P¹[T(V)] = 3 0 0 1 3/2 E [T(v)]=A[v]=3 -1/2 E =

Advanced Engineering Mathematics
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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Let B = {(1, 1, 0), (0, 1, 1), (1, 0, 1)) and B' = {(1, 0, 0), (0, 1, 0), (0, 0, 1)) be bases for R³, and let A = 2 1 be the matrix for T: R³ R³ relative to B. (a) Find the transition matrix P from B' to B. 0 P= 1 [v] = [T(V)] = -1 p-1= (b) Use the matrices P and A to find [v] and [7(v)], where [v] [110]. 1 0 0 4/3 0 = 1/2 41 (c) Find P¹ and A' (the matrix for T relative to B). 900- 000- 0 1 0 1 0 (d) Find [T(v)] two ways. 1 -682 A'= 3/2 -2 -1 [T(v)] = P¹[T(v)] = lo [T(v)] = A[v] = 0 3/2 -1 - -1/2 000-000- -B 1
Transcribed Image Text:Let B = {(1, 1, 0), (0, 1, 1), (1, 0, 1)) and B' = {(1, 0, 0), (0, 1, 0), (0, 0, 1)) be bases for R³, and let A = 2 1 be the matrix for T: R³ R³ relative to B. (a) Find the transition matrix P from B' to B. 0 P= 1 [v] = [T(V)] = -1 p-1= (b) Use the matrices P and A to find [v] and [7(v)], where [v] [110]. 1 0 0 4/3 0 = 1/2 41 (c) Find P¹ and A' (the matrix for T relative to B). 900- 000- 0 1 0 1 0 (d) Find [T(v)] two ways. 1 -682 A'= 3/2 -2 -1 [T(v)] = P¹[T(v)] = lo [T(v)] = A[v] = 0 3/2 -1 - -1/2 000-000- -B 1
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