2. For a linear transformation T: R → R' defined by T(w,x,y,z)=(w+y-z,x-y+z,w+x), which of the following vectors belong to the kernel of T? Circle all appropriate responses and show all your work! a. (1, 1, 1, 1) b. (0, 0, 1, 1) c. (1, 0, 0, -1) d. (0, 0, 0, 0)

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...
icon
Related questions
Question
2. For a linear transformation T: RR³ defined by
T(w,x,y,z)=(w+y-z,x-y+z,w+x), which of the following vectors belong to
the kernel of T? Circle all appropriate responses and show all your work!
a. (1, 1, 1, 1)
b. (0, 0, 1, 1)
c. (1, 0, 0, -1)
d. (0, 0, 0, 0)
Transcribed Image Text:2. For a linear transformation T: RR³ defined by T(w,x,y,z)=(w+y-z,x-y+z,w+x), which of the following vectors belong to the kernel of T? Circle all appropriate responses and show all your work! a. (1, 1, 1, 1) b. (0, 0, 1, 1) c. (1, 0, 0, -1) d. (0, 0, 0, 0)
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning