Find the range and kernel of:(adsbygoogle = window.adsbygoogle || []).push({});

a) T(v1,v2) = (v2, v1)

b) T(v1,v2,v3) = (v1,v2)

c) T(v1,v2) = (0,0)

d) T(v1,v2) = (v1, v1)

Unfortunately the book I'm using (Strang, 4th edition) doesnt even mention these terms and my professor isn't helpful. My professor said:

"Since range and kernel are subspaces of R^2 (in this problem) you need not give a basis but, rather, simply describe the subspace (i.e. plane, line, zero subspace)"

I dont really know what I'm supposed to find. Let's look at d)

I constructed a 2 x 2 matrix:

[1 0][v1] [v1]

[1 0][v2] =[v1]

Up to this point, I'm not sure what to do or if i'm doing this problem right...I'm stuck, please help!

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# Homework Help: Finding range and kernel of linear transformation

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