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...

Extracted 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