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For fixed positive integers m and n, the set Mmxn of all mxn matrices is a vector space, under the usual operations of addition of matrices and multiplication by real scalars. Let F be a fixed 3x2 matrix, and let H be the set of all matrices A in Mzx4 With the property that FA = 0 (the zero matrix in Max4). Determine if H is a subspace of M2 x4- Choose the correct answer below. O A. The set H is not a subspace of M2 x4 because the set is not closed under addition. O B. The set H is not a subspace of M2 x4 because the set is not closed under multiplication by scalars. OC. The set H is not a subspace of M2 x4 because the set does not contain the 2 × 4 zero matrix. O D. The set H is a subspace of M2 x4 because the set contains the 2x4 zero matrix, the set is closed under addition, and the set is closed under multiplication by scalars. O E. The set H is a subspace of M2 x4 because FA = 0 implies that A is the zero matrix, and set H is the trivial subspace {0}.

For fixed positive integers m and n, the set Mmxn of all mxn matrices is a vector space, under the usual operations of addition of matrices and multiplication by real scalars. Let F be a fixed 3x2 matrix, and let H be the set of all matrices A in Mzx4 With the property that FA = 0 (the zero matrix in Max4). Determine if H is a subspace of M2 x4- Choose the correct answer below. O A. The set H is not a subspace of M2 x4 because the set is not closed under addition. O B. The set H is not a subspace of M2 x4 because the set is not closed under multiplication by scalars. OC. The set H is not a subspace of M2 x4 because the set does not contain the 2 × 4 zero matrix. O D. The set H is a subspace of M2 x4 because the set contains the 2x4 zero matrix, the set is closed under addition, and the set is closed under multiplication by scalars. O E. The set H is a subspace of M2 x4 because FA = 0 implies that A is the zero matrix, and set H is the trivial subspace {0}.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.4: Orthogonal Diagonalization Of Symmetric Matrices
Problem 26EQ
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For fixed positive integers m and n, the set Mmxn of all mxn matrices is a vector space, under the usual operations of addition of matrices and multiplication by real scalars. Let F be a fixed 3x2 matrix, and let H be the set of all matrices A in M2 x4 with the property that FA = 0 (the zero matrix in M3x4). Determine if H is a subspace of M2 x4- Choose the correct answer below. O A. The set H is not a subspace of M,x4 because the set is not closed under addition. O B. The set H is not a subspace of M2x4 because the set is not closed under multiplication by scalars. OC. The set H is not a subspace of M2x4 because the set does not contain the 2x4 zero matrix. O D. The set H is a subspace of M, x4 because the set contains the 2x4 zero matrix, the set is closed under addition, and the set is closed under multiplication by scalars. O E. The set H is a subspace of M, x4 because FA=0 implies that A is the zero matrix, and set H is the trivial subspace {0}.
Transcribed Image Text:For fixed positive integers m and n, the set Mmxn of all mxn matrices is a vector space, under the usual operations of addition of matrices and multiplication by real scalars. Let F be a fixed 3x2 matrix, and let H be the set of all matrices A in M2 x4 with the property that FA = 0 (the zero matrix in M3x4). Determine if H is a subspace of M2 x4- Choose the correct answer below. O A. The set H is not a subspace of M,x4 because the set is not closed under addition. O B. The set H is not a subspace of M2x4 because the set is not closed under multiplication by scalars. OC. The set H is not a subspace of M2x4 because the set does not contain the 2x4 zero matrix. O D. The set H is a subspace of M, x4 because the set contains the 2x4 zero matrix, the set is closed under addition, and the set is closed under multiplication by scalars. O E. The set H is a subspace of M, x4 because FA=0 implies that A is the zero matrix, and set H is the trivial subspace {0}.
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