2. Decide if each statement is true or false, and explain why. a) If V₁, V2, ..., Un are linearly independent vectors, t

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2 Decide If Each Statement Is True Or False And Explain Why A If V V2 Un Are Linearly Independent Vectors T 1 (101.65 KiB) Viewed 43 times

2. Decide if each statement is true or false, and explain why. a) If V₁, V2, ..., Un are linearly independent vectors, then Span{₁, 2,..., Un} has dimension n. b) If the matrix equation Ax = 0 has the trivial solution, then the columns of A are linearly independent. c) If Span {1, ₂} is a plane and the set {V1, V2, V3} is linearly dependent, then v3 € Span{v1, v₂}. d) If v3 is not a linear combination of ₁ and 2, then {V1, V2, V3} is linearly independent. e) If {V1, V2, V3} is linearly dependent, then so is {1, 2, 3, } for any vector . f) The set {0} is linearly independent. g) If {V1, V2, V3, V4} is linearly independent, then so is {V1, V2, V3}. h) The collumns of any 4 x 5 matrix are linearly dependent. i) If Az = (2) has only one solution, then the columns of A are linearly independent. j) If Span {V1, V2, V3} has dimension 3, then {V1, V2, V3} is linearly independent.