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## Homework Statement

Matrix A is 3x3

1 -5 -5

-5 1 5

5 -5 -9

Find basis for corresponding eigenspace when eigenvalue is -4

a) 0 b) 1 0 c) 1 d)1 0

1 0 1 0 0 1

-1 1 , -1 -1 -1 , 1

## Homework Equations

(A-lambda I)x=0

## The Attempt at a Solution

(A-(-4I)= 5 -5 -5

-5 5 5

5 -5 -5

that matrix times x will be equal to zero

created augmented matrix: 5 -5 -5 0

-5 5 5 0

5 -5 -5 0

find reduced echelon form of augmented matrix:

1 -1 -1 0

0 0 0 0

0 0 0 0

therefore x

_{1}=x

_{2}+x

_{3}

and x

_{2}and x

_{3}are free

vector x= x

_{2}+x

_{3}

x

_{2}

x

_{3}

which can be reduced to:

x

_{2}*1 + x

_{3}* 1

1 0

0 1

For the basis of the eigenspace, I then get:

1 1

1 0

0 , 1

However, the homework question is multiple choice and this is not one of the options. What am I doing wrong?