Question

Find a basis for Col A and a basis for Nul A.

A) Col A is the column space, and Nul A is the null space.
B) Bases for Col A and Nul A cannot be determined.
C) A basis for Col A is a subset of A's columns, and a basis for Nul A is a subset of A's null space.
D) Col A and Nul A have the same basis.

Answer 1

In linear algebra, the column space (Col A) of a matrix A is the span of its column vectors. The null space (Nul A) of a matrix A is the set of all vectors that, when multiplied by A, yield the zero vector. To find a basis for Col A, we need to find the linearly independent columns of A. To find a basis for Nul A, we need to solve the system of linear equations Ax=0.

Step-by-step explanation:

In linear algebra, the column space (Col A) of a matrix A is the span of its column vectors. To find a basis for Col A, we need to find the linearly independent columns of A. These columns form a basis for Col A.

The null space (Nul A) of a matrix A is the set of all vectors that, when multiplied by A, yield the zero vector. To find a basis for Nul A, we need to solve the system of linear equations Ax=0.

Therefore, the correct answer is option C. A basis for Col A is a subset of A's columns, and a basis for Nul A is a subset of A's null space.