Let be a basis for a subspace . Use the Gram-Schmidt process to find and orthogonal basis for .

Suppose using the Gram-Schmidt process, you found that the set is an orthogonal basis for some subspace . Find an orthonormal basis i for ,



The matrix below has three pivot columns.

First, find a basis for .


Now, use the Gram-Schmidt process to find an orthogonal basis for .

Let . First, find a basis for .


Now, use the Gram-Schmidt process to find an orthogonal basis for .

The column space of is only two dimensional in this problem. How do you find a basis for ?