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## Homework Statement

Given that A is an 13 × 11 matrix of rank 3.

a)The nullspace of A is a d-dimensional subspace of Rn.

What is the dimension, d, and n of Rn?

b) Is it true that for every b ∈ R11, the system ATx = b is consistent? (What does this means?)

## The Attempt at a Solution

The row space has d = 3, n = 11

The col space has d =3, n = 13

The rows aren't linearly independent. The columns aren't linearly independent.

The nullity of A is 8. (n =11; 11 - rank 3 = 8)

a)

The row space has d = 3, n = 11

The col space has d =3, n = 13

The rows aren't linearly independent. The columns aren't linearly independent.

The nullity of A is 8. (n =11; 11 - rank 3 = 8)

How do I find d and n of Rn?

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