# Algebra Examples

Step 1

Step 1.1

Swap with to put a nonzero entry at .

Step 1.2

Multiply each element of by to make the entry at a .

Step 1.2.1

Multiply each element of by to make the entry at a .

Step 1.2.2

Simplify .

Step 1.3

Swap with to put a nonzero entry at .

Step 1.4

Multiply each element of by to make the entry at a .

Step 1.4.1

Multiply each element of by to make the entry at a .

Step 1.4.2

Simplify .

Step 2

The row space of a matrix is the collection of all possible linear combinations of its row vectors.

Step 3

The basis for is the non-zero rows of a matrix in reduced row echelon form. The dimension of the basis for is the number of vectors in the basis.

Basis of :

Dimension of :