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1. For each of the statements below, State whether it is true or false, and Motivate with either a proof, a reference to a definition or theorem, or a counterexample. your answer W1 (a) Let A be an (m x n)-matrix. Write A:= [V1- Vn) = .... Wm If {V1, V2} forms a basis for col(A), then {w1, W2} forms a basis for row(A). (b) Let A, B be (m x n)-matrices over R. If A and B are row equivalent, then row(A) = row(B) and col(A) = col(B). (c) The set { [a 0 0]: a ER} is a 1-dimensional subspace of R. 31 1 17 (d) Let A := 2 and v := [1 22 1. Then, uE col(A) and v e row(A). 1 1 2 u := 2123

1. For each of the statements below, State whether it is true or false, and Motivate with either a proof, a reference to a definition or theorem, or a counterexample. your answer W1 (a) Let A be an (m x n)-matrix. Write A:= [V1- Vn) = .... Wm If {V1, V2} forms a basis for col(A), then {w1, W2} forms a basis for row(A). (b) Let A, B be (m x n)-matrices over R. If A and B are row equivalent, then row(A) = row(B) and col(A) = col(B). (c) The set { [a 0 0]: a ER} is a 1-dimensional subspace of R. 31 1 17 (d) Let A := 2 and v := [1 22 1. Then, uE col(A) and v e row(A). 1 1 2 u := 2123

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.3: Orthonormal Bases:gram-schmidt Process
Problem 17E: Complete Example 2 by verifying that {1,x,x2,x3} is an orthonormal basis for P3 with the inner...
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please help me with 1a to d

1. For each of the statements below, State whether it is true or false, and Motivate your answer with either a proof, a reference to a definition or theorem, or a counterexample. (a) Let A be an (m x n)-matrix. Write A := [v1 ... Vn] = W1 If {V1, V2} forms a basis for col(A), then {w1, W2} forms a basis for row (A). (b) Let A, B be (m x n)-matrices over R. If A and B are row equivalent, then row(A) row(B) and col(A) = col(B). (c) The set { [a 0 0] : a E R} is a l-dimensional subspace of R. 1 1 1 2 1 (d) Let A:= 1 and v := [1 2 2 1]. Then, u E col(A) and v row(A). ,u := 1 23
Transcribed Image Text:1. For each of the statements below, State whether it is true or false, and Motivate your answer with either a proof, a reference to a definition or theorem, or a counterexample. (a) Let A be an (m x n)-matrix. Write A := [v1 ... Vn] = W1 If {V1, V2} forms a basis for col(A), then {w1, W2} forms a basis for row (A). (b) Let A, B be (m x n)-matrices over R. If A and B are row equivalent, then row(A) row(B) and col(A) = col(B). (c) The set { [a 0 0] : a E R} is a l-dimensional subspace of R. 1 1 1 2 1 (d) Let A:= 1 and v := [1 2 2 1]. Then, u E col(A) and v row(A). ,u := 1 23
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