(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let T: R3 --> R3 be the linear transformation that projectsuontov= (3,0,4)

Find the rank and nullity of T

2. Relevant equations

So letu=(x,y,z)

3. The attempt at a solution

So I know that

T(u) = proj. u onto v

T(u) = [(3x + 4z)/ 25](3,0,4)

T(u) =0

This is where I get confused, in a simalar example from my text (which skips some steps) leads me to belive that I can set 3x + 4z = 0.

Is not the nullity(T) = dim(ker(T))?

So would'nt I have to

T(u) = [(3x + 4z)/ 25](3,0,4) = (0,0,0)

Create an augmented matrix and find the nullspace?

I get a different answer than the book is getting?

Any ideas?

Rob

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Linear Transformation rank and nullity

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