# Finding the orthonormal basis of U = Col(A) (A is a matrix)

Let

A = $\begin{bmatrix}1&7&6\\2&6&4\\4&3&-1\end{bmatrix}$

and U = Col(A). Find the orthonormal basis for U.

Am I supposed to designate vectors $x_1, x_2, x_3$ as the columns of A, and then, perform the Gram-Schmidt algorithm using those vectors? I tried that but ended up with a 0 vector, and that wouldn't form a basis. What am I doing wrong?

• I’ve got a slight quibble with the wording of the problem: there is an infinite number of orthonormal bases for $U$—asking for the basis isn’t well-defined. – amd Mar 2 '16 at 3:39