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## Homework Statement

Use the given information to find the nullity of T and give a geometric description of the kernel and range of T.

T is the projection onto the vector v = (1,2,2):

T(x,y,z) = (x + 2y + 2z)/9 (1,2,2)

## Homework Equations

Kernel of T = T(v) = 0.

Nullity of T = dimension of the kernel of T

## The Attempt at a Solution

I created an augmented matrix that looks like this:

[ 1/9 2/9 2/9 | 1

2/9 4/9 4/9 | 2

2/9 4/9 4/9 | 2 ]

Row reducing I get just one vector because the other two are a scalar.

However, the answer in the book says the nullity is 2, so I am off.