In Exercises 1-4, W is a subspace of the vector space V of all (2 x 2) matrices. A matrix A in W is written as a b ^=[%] A c d In each case exhibit a basis for W. 1. W = {A: a+b+c+d=0} 2. W = {A: a = -d, b=2d, c = -3d} 3. W = {A: a = 0} 4. W = {A: b = a - c, d = 2a + c}
In Exercises 1-4, W is a subspace of the vector space V of all (2 x 2) matrices. A matrix A in W is written as a b ^=[%] A c d In each case exhibit a basis for W. 1. W = {A: a+b+c+d=0} 2. W = {A: a = -d, b=2d, c = -3d} 3. W = {A: a = 0} 4. W = {A: b = a - c, d = 2a + c}
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![In Exercises 1-4, W is a subspace of the vector space V
of all (2 x 2) matrices. A matrix A in W is written as
A
^ = []
In each case exhibit a basis for W.
1. W = {A: a+b+c+d=0}
2. W = {A: a = -d, b=2d, c = -3d}
3. W = {A: a = 0}
4. W = {A: b = a - c, d = 2a + c}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffb989860-4d1c-4fb5-9e6b-42a4528dce9c%2F0d417e36-fdd8-4b39-b32a-1d476fa80ee8%2Feld8mtw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In Exercises 1-4, W is a subspace of the vector space V
of all (2 x 2) matrices. A matrix A in W is written as
A
^ = []
In each case exhibit a basis for W.
1. W = {A: a+b+c+d=0}
2. W = {A: a = -d, b=2d, c = -3d}
3. W = {A: a = 0}
4. W = {A: b = a - c, d = 2a + c}
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