HW-8-Solutions

# Linear transformations consider example 1 given on

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Unformatted text preview: present any linear transformation as a matrix. a. Find the matrix representation of linear transformation that does the rotation of the vector about the origin by 90o clockwise. That is, find such that is the vector o rotated 90 about the origin clockwise. b. Find the matrix representation of the transformation which does rotation about the origin for an arbitrary angle, . Solution a. b. ([ ]) ([ ]) [ [ ] [ () () () () 4. Linear Transformations Consider Example 3 on page 23. Find the P matrix and verify that Need to solve ̅ [ Solving this similar to problem 1 gives 7 December 2012 [ [ 6 ̅ . . Dept. of ECE, Drexel University ECE-S511: Systems I Fall 2012-2013 5. Linear Transformations – Example 4 pg. 24 You may use MATLAB or some other numerical tool to assist you in the computations. Consider the following matrix representation of a linear operator: [ a. Find the rank and nullity of the matrix A. b. Choose an appropriate vector b to be used to compute the companion form of the matrix A. (Hint: Choose something simple as Example 4 did.) c. Verify that qualify to form a basis. What condition must be satisfied? d. Write the representation of w.r.t. the basis . e. Find the change of basis matrix Q and verify that ̅ . Solution a. Rank = 4, Nullity = 0 [ b. c. [ [ , which has rank 4. Therefore all columns are linearly independent and this qualifies as a basis. d. [ e. Same as part c. 7 December 2012 7 Dept. of ECE, Drexel University...
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