Question

Find a basis for the column space of the matrix.
B=[1 -2 4 4; 2 -4 11 4; -3 6 -12 12]

Answer 1

To find a basis for the column space of matrix B, we need to determine which columns are linearly independent.

Step-by-step explanation:

To find a basis for the column space of the matrix B, we need to find the column vectors that are linearly independent. The column space consists of all linear combinations of the column vectors.

First, let's write the matrix B as a system of equations:

[1 -2 4 4; 2 -4 11 4; -3 6 -12 12]

The row-reduced echelon form of B can help us determine which columns are linearly independent. After row operations, we get:

[1 0 2 0; 0 1 3 0; 0 0 0 1]

The pivot columns are the first and second columns. Therefore, a basis for the column space of B is the set of columns corresponding to the pivot columns:

{[1 2; 2 3; -3 0]}