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# m235_f11prac-page2 - 5 True or False You must explain the...

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5. True or False. You must explain the reason for your answer. a: If a matrix M is invertible, then kernel of M is just the zero vector. b: If u, v, w 2 V, V a subspace of R n , then the vector 2 u - 3 v + 4 w is also an element of V. c: If a 5 by 5 matrix A has rank 5 , then any linear system of equations with coe ffi cient matrix A will have a unique solution. d: There exists a 2 2 matrix B so that B 1 1 = 1 2 , and B 2 2 = 2 1 . e: Let A be a matrix of size 3 5. Assume that the equation Ax = 0 @ 1 2 4 1 A has a solution. Then it has infinitely many solutions.
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