Let V be the subspace of R' spanned by vi = (1, 3, -2, 2, 3 ), v (1, 4, -3, 4, 2 ), v3 (1, 3, 0, 2, 3) and W be the subspace spanned by w, ( 2, 3,-1, -2,9), w, (1, 5, -6, 6, 1 ), wy (2, 4, 4, 2, 8). Find a basis for V + W and VOw. Let T(x, y, z) (x-y+z, x + 2), S(x, y) (x, x-y, y) be two transformations. a) Find S T or T•S whenever it is defined and find the matrix representation [S Ta, where a = ((1, 1, 1), (1, 1, 0), (1, 0, 0)) and Bß (1, 0, 0), (0, 1, 0), (0, 0, 1)). shies
Let V be the subspace of R' spanned by vi = (1, 3, -2, 2, 3 ), v (1, 4, -3, 4, 2 ), v3 (1, 3, 0, 2, 3) and W be the subspace spanned by w, ( 2, 3,-1, -2,9), w, (1, 5, -6, 6, 1 ), wy (2, 4, 4, 2, 8). Find a basis for V + W and VOw. Let T(x, y, z) (x-y+z, x + 2), S(x, y) (x, x-y, y) be two transformations. a) Find S T or T•S whenever it is defined and find the matrix representation [S Ta, where a = ((1, 1, 1), (1, 1, 0), (1, 0, 0)) and Bß (1, 0, 0), (0, 1, 0), (0, 0, 1)). shies
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 V be the subspace of R' spanned by v, (1, 3, -2, 2, 3 ), v2 ( 1, 4, -3, 4, 2 ), v3 =(1, 3, 0, 2, 3 )
and W be the subspace spanned by w, ( 2, 3, -1,-2, 9 ), w, (1, 5, -6, 6, 1 ), w, ( 2, 4, 4, 2, 8).
Find a basis for V + W and VOw.
Let T(x, y, z) (x-y+z, x +2), S(x, y) = (x, x-y, y) be two transformations.
a) Find S T or T•S whenever it is defined and find the matrix representation [S Ta, where
a = (1, 1, 1), (1, 1, 0), (1, 0, 0)} and B = ((1, 0, 0), (0, 1, 0), (0, 0, 1)).
b) Prove or disprove S-T is an isomorphism.
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd33b780d-79f4-4239-b5c1-33d9c6a1f109%2Fa5a774f0-65d3-4151-8ca2-beda2f029cbf%2Fz0z8f9s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let V be the subspace of R' spanned by v, (1, 3, -2, 2, 3 ), v2 ( 1, 4, -3, 4, 2 ), v3 =(1, 3, 0, 2, 3 )
and W be the subspace spanned by w, ( 2, 3, -1,-2, 9 ), w, (1, 5, -6, 6, 1 ), w, ( 2, 4, 4, 2, 8).
Find a basis for V + W and VOw.
Let T(x, y, z) (x-y+z, x +2), S(x, y) = (x, x-y, y) be two transformations.
a) Find S T or T•S whenever it is defined and find the matrix representation [S Ta, where
a = (1, 1, 1), (1, 1, 0), (1, 0, 0)} and B = ((1, 0, 0), (0, 1, 0), (0, 0, 1)).
b) Prove or disprove S-T is an isomorphism.
%3D
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