HW-8-Solutions

HW-8-Solutions

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Unformatted text preview: or gives 3 equations with 5 unknowns, so we are free to pick 2 variables (Note not necessarily any two). The 3 equations are: 7 December 2012 4 Dept. of ECE, Drexel University ECE-S511: Systems I Choosing Choosing Fall 2012-2013 gives: . gives: . These vectors are linearly independent and therefore serve as a basis for the nullspace of A3. d. The rank of is 3, therefore a basis for the column space is: [ ] [ ] [ ] A basis for the column space of is the set of the 2 linearly independent columns of which is: {[ ] [ ]} . The rank of is 3, therefore there are 3 linearly independent columns. These can serve as a basis for the column space of . We can search linearly independent columns from and quickly see that columns 1,2 and 4. Thus a valid basis for the column space is: {[ ] [ ] [ ]}. 7 December 2012 5 Dept. of ECE, Drexel University ECE-S511: Systems I Fall 2012-2013 3. Linear Transformations. Consider Example 1 given on page 20 of Chen. This example showed graphically that rotation about the origin is a linear transformation. As we know, one can re...
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This document was uploaded on 04/04/2014.

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