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L A linear tcansfo,mation T does the following ii, ~ [ ] ➔ [ : ] and ii, ~ [ 7 ] ➔ [ : ] · Find the following. (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. 1 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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Linear Algebra Problems
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