Use Theorem 6.1.4 from the textbook to find the standard matrix for the linear transformation T: R + R? which reflects projects that vector onto the y-axis, and then compresses that vector by a factor of - in the y-direction. vector about the line y = -x, then [T] = Theorem 6.1.4 Let T: R"→ R" be a linear transformation, and suppose that vectors are expressed in column form. If e1, e2, . , en are the standard unit vectors in R", and if x is any vector in R", then T (x) can be expressed as T(x) = Ax (13) where s nolinlo A = [T(ej) T(e2) T(e,)] ...
Use Theorem 6.1.4 from the textbook to find the standard matrix for the linear transformation T: R + R? which reflects projects that vector onto the y-axis, and then compresses that vector by a factor of - in the y-direction. vector about the line y = -x, then [T] = Theorem 6.1.4 Let T: R"→ R" be a linear transformation, and suppose that vectors are expressed in column form. If e1, e2, . , en are the standard unit vectors in R", and if x is any vector in R", then T (x) can be expressed as T(x) = Ax (13) where s nolinlo A = [T(ej) T(e2) T(e,)] ...
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.6: The Matrix Of A Linear Transformation
Problem 18EQ
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![Use Theorem 6.1.4 from the textbook to find the standard matrix for the linear transformation T : R? → R? which reflects a vector about the line y = -x, then
projects that vector onto the y-axis, and then compresses that vector by a factor of - in the y-direction.
[T] =
Theorem 6.1.4 Let T: R"→ R" be a linear transformation, and suppose that vectors are
expressed in column form. If e1, e2, . , en are the standard unit vectors in R", and if x is
any vector in R" , then T (x) can be expressed as
..,
T (x) = Ax
il i
(13)
where
nolulo
A = [T(ej) T(e2)
T(e,)]
...](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F74828714-5251-476a-9f27-78eeedeba02f%2F22f844f3-b7cd-4978-a54b-a349fe6d3973%2F33qa909_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Use Theorem 6.1.4 from the textbook to find the standard matrix for the linear transformation T : R? → R? which reflects a vector about the line y = -x, then
projects that vector onto the y-axis, and then compresses that vector by a factor of - in the y-direction.
[T] =
Theorem 6.1.4 Let T: R"→ R" be a linear transformation, and suppose that vectors are
expressed in column form. If e1, e2, . , en are the standard unit vectors in R", and if x is
any vector in R" , then T (x) can be expressed as
..,
T (x) = Ax
il i
(13)
where
nolulo
A = [T(ej) T(e2)
T(e,)]
...
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