L A linear tcansfo,mation T does the following ii, ~ [ ] ➔ [ : ] and ii, ~ [ 7 ] ➔ [ : ] · Find
(a) Find the matrix which represents this transformation.
(b) Find the coefficient vector which gives b = [ ] as a linear combination of the input
basis vectors v1 and v2 above.
(c) Now use your transformation on your vector from part (b) to get the output vector for b.
2. Given the transformation T(x) = Ax where A= [ ] find a matrix for the linear
0 3 9
transformation which uses the "best" basis for the input and output spaces.
3. Let A = [ 5 -1 ] . Find the the pseudoinverse of A .
4. Suppose a linear transformation is given by T(c) = Ac where A= [ ] . Find the
kernel of T.
5. If T(x) = Ax where A = [ ] , find a matrix which transforms the output basis to
bi = [ 1 ] and b2 = [ ]
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