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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
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
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 ̅
a. Rank = 4, Nullity = 0
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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- Spring '14