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}
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: please solve all parts correctly and handwritten to get instant like
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
- [:$]
d
In each case exhibit a basis for W.
1. W = {A: a+b+c+d=0}
2. W = {A: a = -d, b=2d, c = -3d}
3. W = {A: a = 0}
4. W = {A: b = a - c, d = 2a+c}
Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.
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![In Exercises 1-4, W is a subspace of the vector space V
of all (2 x 2) matrices. A matrix A in W is written as
A
a b
- [:$]
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}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F51e54363-29bc-4d10-90d7-74692f0d2de6%2F13c490bf-96f3-4618-ada4-fe8ab72cd4fe%2F1jt5hs_processed.jpeg&w=3840&q=75)
