Let T : R? → R³ be a linear transformation such that T(x, y) = (y, 2x, x + y). (a) Find the standard matrix A for the linear transformation. (b) Use A to find the image of the vector v = (c) Find the matrix A' relative to B (1, 2). = {(1, 1), (1, 0)} and B' = {(1,0, 0), (1, 1,0), (1, 1, 1)}. (d) Use A' to find [T(v)]; where v = (1,2).
Let T : R? → R³ be a linear transformation such that T(x, y) = (y, 2x, x + y). (a) Find the standard matrix A for the linear transformation. (b) Use A to find the image of the vector v = (c) Find the matrix A' relative to B (1, 2). = {(1, 1), (1, 0)} and B' = {(1,0, 0), (1, 1,0), (1, 1, 1)}. (d) Use A' to find [T(v)]; where v = (1,2).
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 T : R? → R³ be a linear transformation such that T(x, y) = (y, 2x, x + y).
(a) Find the standard matrix A for the linear transformation.
(b) Use A to find the image of the vector v =
= (1, 2).
(c) Find the matrix A' relative to B = {(1,1), (1,0)} and B' = {(1,0,0), (1, 1,0), (1, 1, 1)}.
(d) Use A' to find [T(v)]R where v =
(1, 2).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff57fbb07-e1bd-418f-9d01-1252f5b1cb71%2F5d2c115d-1acd-405f-b0af-9d84b4f4b8ff%2Fxp9q5rw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let T : R? → R³ be a linear transformation such that T(x, y) = (y, 2x, x + y).
(a) Find the standard matrix A for the linear transformation.
(b) Use A to find the image of the vector v =
= (1, 2).
(c) Find the matrix A' relative to B = {(1,1), (1,0)} and B' = {(1,0,0), (1, 1,0), (1, 1, 1)}.
(d) Use A' to find [T(v)]R where v =
(1, 2).
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