Section 1.9 Problem 7. Mark each statement True or False, and justify your answer. (T/F) A linear transformation T:R"+R is completely determined by its effect on the columns of the nxn identity matrix. (T/F) If T:R³-R² rotates vectors about the origin through an angle , then T is a linear transformation. (T/F) The columns of the standard matrix for a linear transformation from R to R are the images of the columns of the nxn identity matrix.
Section 1.9 Problem 7. Mark each statement True or False, and justify your answer. (T/F) A linear transformation T:R"+R is completely determined by its effect on the columns of the nxn identity matrix. (T/F) If T:R³-R² rotates vectors about the origin through an angle , then T is a linear transformation. (T/F) The columns of the standard matrix for a linear transformation from R to R are the images of the columns of the nxn identity matrix.
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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![Section 1.9
Problem 7. Mark each statement True or False, and justify your answer.
(T/F) A linear transformation T:R"→R" is completely determined by its effect on the columns of the nxn
identity matrix.
(T/F) If T:R² R² rotates vectors about the origin through an angle . then T is a linear transformation.
(T/F) The columns of the standard matrix for a linear transformation from R to R are the images of the
columns of the nxn identity matrix.
(T/F) When two linear transformations are performed one after another, the combined effect may not
always be a linear transformation.
(T/F) A mapping T:R"R" is onto R if every vector x in R" maps onto some vector in R™.
(T/F) The standard matrix of a linear transformation from R² to R² that reflects points through the
horizontal axis, the vertical axis, or the origin has the form [2]. where a and d are ±1.
(T/F) A is a 3x2 matrix, then the transformation x-Ax cannot be one-to-one.
(T/F) A is a 3x2 matrix, then the transformation x-Ax cannot map R² onto R³.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe37523b4-8106-408f-9300-625624498825%2Fd667341d-d25c-45be-9542-4387beb65147%2F3bzutlp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Section 1.9
Problem 7. Mark each statement True or False, and justify your answer.
(T/F) A linear transformation T:R"→R" is completely determined by its effect on the columns of the nxn
identity matrix.
(T/F) If T:R² R² rotates vectors about the origin through an angle . then T is a linear transformation.
(T/F) The columns of the standard matrix for a linear transformation from R to R are the images of the
columns of the nxn identity matrix.
(T/F) When two linear transformations are performed one after another, the combined effect may not
always be a linear transformation.
(T/F) A mapping T:R"R" is onto R if every vector x in R" maps onto some vector in R™.
(T/F) The standard matrix of a linear transformation from R² to R² that reflects points through the
horizontal axis, the vertical axis, or the origin has the form [2]. where a and d are ±1.
(T/F) A is a 3x2 matrix, then the transformation x-Ax cannot be one-to-one.
(T/F) A is a 3x2 matrix, then the transformation x-Ax cannot map R² onto R³.
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