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 $$ is only two dimensional in this problem. How do you find a basis for $$?