Let L: R4 → R³ be the linear transformation defined by L((w, x, y, z)) = (w+x, y+z, w+y). a. Find a basis for ker L. What is dim(ker L)? b. Find a basis for im L. What is dim(im L)? c. Is L one-to-one? d. Is L onto?
Let L: R4 → R³ be the linear transformation defined by L((w, x, y, z)) = (w+x, y+z, w+y). a. Find a basis for ker L. What is dim(ker L)? b. Find a basis for im L. What is dim(im L)? c. Is L one-to-one? d. Is L onto?
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 6CM: Let T:R4R2 be the linear transformation defined by T(v)=Av, where A=[10100101]. Find a basis for a...
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please solve (c) and (d) part
![Let L: R4 → R³ be the linear transformation defined by L((w,x, y, z)) = (w+x,y+z, w+y).
a. Find a basis for ker L. What is dim(ker L)?
b. Find a basis for im L. What is dim(im L)?
c. Is L one-to-one?
d. Is L onto?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F66b9d86e-4fe5-4a17-b6ac-06d284c151d2%2Ff8c99d1d-c39f-4aa5-91c9-e8fdbac1a7f8%2Fkzcxhk_processed.png&w=3840&q=75)
Transcribed Image Text:Let L: R4 → R³ be the linear transformation defined by L((w,x, y, z)) = (w+x,y+z, w+y).
a. Find a basis for ker L. What is dim(ker L)?
b. Find a basis for im L. What is dim(im L)?
c. Is L one-to-one?
d. Is L onto?
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