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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 b -=[2] d 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}

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 -=[2] d 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}

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.1: Vector Spaces And Subspaces
Problem 26EQ: In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=3, W={[aba+b+1]}
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Linear algebra: please solve all parts correctly and handwritten to get instant like
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 a b - [:$] d In each case exhibit a basis for W. 1. W = {A: a+b+c+d=0} 2. W = {A: a = -d, b=2d, c = -3d} 3. W = {A: a = 0} 4. W = {A: b = a - c, d = 2a+c}
Transcribed Image Text:In Exercises 1-4, W is a subspace of the vector space V of all (2 x 2) matrices. A matrix A in W is written as A a b - [:$] 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}
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