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## Homework Statement

part a.

Use the matrix A =

{[1,-1,0]

[0,-1,1]

[-1,2,-1]}

to compute T(x) for x =

{[1]

[2]

[3]}

Here, T:R^3-->R^3 is defined as T(x)=Ax.

part b.

describe the kernel of the transformation.

part c.

what is the nullity of the tarnsformation

part d.

what is the rank of the transformation

## Homework Equations

I guess the only equation is the rank nullity theorum, and T(x)=Ax

## The Attempt at a Solution

a.

i multiplied the matrix A and x and got

T(x)=

{[-1]

[1]

[0]}

this part wasn't too hard.

b.

the kernel is the solution of Ax=0, right?

i solved the matrix equation and got ker T=

{[t]

[t]

[t]}

Is this correct?

c. the nullity is the dimension of the kernel space, so is it 1?? (i am guessing)

d. the dimension of the space is 3, so the rank is 2?? according to the rank nullity theorum?? (once again, guessing)

I'm sure i am doing something wrong. what is the logic behind parts c and d?