Question: 5. (8 points) True or False (a) A subset H of a vector space V is a subspace of V if the zero vector is

5. (8 points) True or False (a) A subset H of a vector space V is a subspace of V if the zero vector is in H. (b) If A is a 4 x 5 matrix then the solution space of Ax = 0 is a subspace of IR5. (c) If dimV = n and if S is linearly independent, then S is a basis of V. (d) The dimension of the null space of A is the number of columns of A that are not pivot columns. (e) In some cases, a plane in RS can be isomorphic to IR2. 6. (14 points) Let 7: " - I'm be a linear transformation. Let A be a matrix representation. [a + 2b - c] (a) Find a 3x3 matrix A given ColA b +c :a,b,c real La + b - 2c] (b) Find the Kernel of T and its dimension. (c) Find the Range of T and its dimension

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