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8. Consider a 4 × 2 matrix A and a 2 × 5 matrix B ....

8. Consider a 4 × 2 matrix A and a 2 × 5 matrix B .

(a) What are the possible dimensions of the null space of AB? Justify your answer.

(b) What are the possible dimensions of the range of AB Justify your answer.

(c) Can the linear transformation define by A be one to one? Justify your answer.

(d) Can the linear transformation define by B be onto? Justify your answer.

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