Find an Orthonormal Basis for Linear Algebra A

[Bob]

$$A=\left(\begin{array}{cc}\frac{1}{2}&-\frac{1}{2}\\\frac{1}{2}&-\frac{1}{2}\\\frac{1}{2}&\frac{1}{2}\\\frac{1}{2}&\frac{1}{2}\end{array}\right)$$

Find an orthonomal basis for N(A^T)

 

[matt grime]

What is N(A^T)? I know what A^T means, but what does the N of it mean?

 

[HallsofIvy]

The null space. The set of all vector, v, such that A^Tv= 0.

Bob, write v as (a, b, c, d) and write out the two equations corresponding to A^Tv= 0. Simplify them.