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1. Let L: R R' be defined by L(r, y) (r - y,0, r+y). (a) Show that L is a linear transformation. (b) What is the kernel of L? (c) What is the nullity of L?

1. Let L: R R' be defined by L(r, y) (r - y,0, r+y). (a) Show that L is a linear transformation. (b) What is the kernel of L? (c) What is the nullity of L?

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.2: The Kernewl And Range Of A Linear Transformation
Problem 59E: Let T:R3R3 be the linear transformation that projects u onto v=(2,1,1). (a) Find the rank and...
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answer a b c only first 3 sub questions
1. Let L: R? → R' be defined by L(r, y) (r- y. 0, r + y). (a) Show that L is a linear transformation. (b) What is the kernel of L? (c) What is the nullity of L? (d) What is the rank of L? (e) Consider the bases B, = {(1,2). (1, 1)} and B = {(1, 1, 1), (1, 1,0). (0. 1, 1)} of R? and R', respectively. Determine the matrix A for L relative to the non-standard bases B, and B2, and find L(-3,2). %3D (f) If B, and B2 are the standard bases, what is the matrix A of L relative to these bases? What is L(-3, 2)? CS Seassed with CamScaniner
Transcribed Image Text:1. Let L: R? → R' be defined by L(r, y) (r- y. 0, r + y). (a) Show that L is a linear transformation. (b) What is the kernel of L? (c) What is the nullity of L? (d) What is the rank of L? (e) Consider the bases B, = {(1,2). (1, 1)} and B = {(1, 1, 1), (1, 1,0). (0. 1, 1)} of R? and R', respectively. Determine the matrix A for L relative to the non-standard bases B, and B2, and find L(-3,2). %3D (f) If B, and B2 are the standard bases, what is the matrix A of L relative to these bases? What is L(-3, 2)? CS Seassed with CamScaniner
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