HW-8-Solutions

a very similar treatment wrt to

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Unformatted text preview: ]) will yield an associated change of basis operator and the representation of the linear operator w.r.t. the basis 7 December 2012 2 [ is: Dept. of ECE, Drexel University ECE-S511: Systems I Fall 2012-2013 [ Now to show that and are similar. One way is to solve the algebraic equation directly for an arbitrary matrix [ [ as follows: This gives 4 unknowns and 4 equations: Solving these equations gives one matrix for as: [ Note: There are infinitely many solutions for this problem. 7 December 2012 3 Dept. of ECE, Drexel University ECE-S511: Systems I Fall 2012-2013 2. Solution a. ( ) ( ) and ( ) . One can easily check these by doing simple row reduction of each matrix. b. From the answer to part (a) above, we can automatically determine the nullity: () () and . c. A basis for the null space of A basis for the null space of [. is trivial, and is [ can be found by solving ( ) , . for non-zero to give: A basis for the null space of can also be found by solving for non-zero . Assume an arbitrary vector [ . Writing out the equations f...
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