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:
. 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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