Please help me answer the following T/F questions. Let M be the space of all 2 T

Question

Please help me answer the following T/F questions.

Let M be the space of all 2 Times 2 matrices. The smallest subspace that contains and is the set of all matrices that can be written as with real numbers s and t. If S and T are subspaces of the same vector space, then so is their intersection. If S and T are subspaces of the same vector space, then so is their union. If the 9 by 12 system Ax = b is solvable for every b then the column space of A is all of R12. Suppose A and B are both n Times n. If B is invertible then the column space of AB is the same as the column space of A. Suppose A and B are both n Times n. If A is invertible then the column space of AB is the same as the column space of B. If A is any 5 by 5 invertible matrix then its column space is R5 . For the last two items see problem 31 on page 131. If S is the column space of A and T is the column space of B then S + T is the column space of A + B. If S is the column space of A and T is the column space of B then S + T is the column space of the block matrix [A B] Note: In order to get credit for this problem all answers must be correct.

Explanation / Answer

1) True

2) True

3) True

4) True

5) True

6) False

7) True

8) False

9) True

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