Solved: State with a brief explanation whether the following statements are true or
Chapter 1, Problem 7(choose chapter or problem)
State with a brief explanation whether the following statements are true or false. (a) The set {(1, 0, 0), (0, 1, O)} is the basis for a twodimensional subspace of R3 (b) The set { (1, 0, 0)} is the basis for a one-dimensional subspace of R3. (c) The vector (a, 2a, b) is an arbitrary vector in the plane spanned by the vectors (1, 2, 0) and (0, 0, 1). (d) The vector (a, b, 2a - b) is an arbitrary vector in the plane spanned by the vectors (1, 0, 2) and {O, 1, -1). (e) The set {(1, 0, 0), (0, 1, 0), (1, 1, O)} is a basis for a subspace ofR3 (f) R2 is a subspace of R3
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