Question

11. If the null space of an 8 × 5 matrix A is 2-dimensional, what is the dimension of the row space of A? 12. If the null space of a 5 × 6 matrix A is 4-dimensional, what is the dimension of the row space of A? 13. If A is a 7 × 5 matrix, what is the largest possible rank of A? If A is a 5 × 7 matrix, what is the largest possible rank of A? Explain your answers. 14. If A is a 4 × 3 matrix, what is the largest possible dimension of the row space of A? If A is a 3 × 4 matrix, what is the largest possible dimension of the row space of A? Explain. 15. If A is a 6 × 8 matrix, what is the smallest possible dimension of Nul A?

          11. If the null space of an 8 × 5 matrix A is 2-dimensional, what is the dimension of the row space of A?
12. If the null space of a 5 × 6 matrix A is 4-dimensional, what is the dimension of the row space of A?
13. If A is a 7 × 5 matrix, what is the largest possible rank of A?
If A is a 5 × 7 matrix, what is the largest possible rank of A?
Explain your answers.
14. If A is a 4 × 3 matrix, what is the largest possible dimension of the row space of A? If A is a 3 × 4 matrix, what is the largest possible dimension of the row space of A? Explain.
15. If A is a 6 × 8 matrix, what is the smallest possible dimension of Nul A?

11. If the null space of an 8 × 5 matrix A is 2-dimensional, what is the dimension of the row space of A?
12. If the null space of a 5 × 6 matrix A is 4-dimensional, what is the dimension of the row space of A?
13. If A is a 7 × 5 matrix, what is the largest possible rank of A?
If A is a 5 × 7 matrix, what is the largest possible rank of A?
Explain your answers.
14. If A is a 4 × 3 matrix, what is the largest possible dimension of the row space of A? If A is a 3 × 4 matrix, what is the largest possible dimension of the row space of A? Explain.
15. If A is a 6 × 8 matrix, what is the smallest possible dimension of Nul A?

Added by Jesse W.

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