Let A be a 3 × 3 matrix, and let v1, V2, V3 be non-zero vectors in R³. Suppose that Av1 = V1, Av2 2v2 and Av3 = 0. Using the above information, determine whether each of the following statements is true or false. EITHER WAY, briefly justify your answer. This might be a short explanation or, if false, an example that shows it is false. (a) A is invertible. (b) A is diagonalizable. (c) {V1, V2, V3} is linearly independent. (a) Tho chorootoristie oguetion of A is 13 12

Elementary Linear Algebra (MindTap Course List)
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Chapter2: Matrices
Section2.1: Operations With Matrices
Problem 77E
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Let A be a 3 × 3 matrix, and let v1, V2, V3 be non-zero vectors in R³. Suppose that
Avi
= V1,
Av2 = 2v2
and
Av3 = 0.
Using the above information, determine whether each of the following statements is
true or false. EITHER WAY, briefly justify your answer. This might be a short
explanation or, if false, an example that shows it is false.
(a) A is invertible.
(b) A is diagonalizable.
(c) {V1, V2, V3} is linearly independent.
(d) The characteristic equation of A is –X² – 2A = 0
Transcribed Image Text:Let A be a 3 × 3 matrix, and let v1, V2, V3 be non-zero vectors in R³. Suppose that Avi = V1, Av2 = 2v2 and Av3 = 0. Using the above information, determine whether each of the following statements is true or false. EITHER WAY, briefly justify your answer. This might be a short explanation or, if false, an example that shows it is false. (a) A is invertible. (b) A is diagonalizable. (c) {V1, V2, V3} is linearly independent. (d) The characteristic equation of A is –X² – 2A = 0
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