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hw2-solutions

hw2-solutions - Assignment 2 Matrix Equations and Linear...

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Assignment 2: Matrix Equations and Linear Independence Written by: Saber Mirzaei Problem 1. The augmented matrix is: [ ] [ ] Using rref function to find the Reduced Row Echelon form: ( ) [ ] Translating back to equation for: Hence: [ ] [ ] [ ] [ ] [ ]
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Problem 2. The augmented matrix is: [ ] [ ] Using rref function: ( ) [ ] Translating back to equation for: Hence: [ ] [ ] [ ] [ ]
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Problem 3. The set of three vectors ( ) ( ) and ( ) are independent iff the following equation has only one solution (which is the trivial one): [ ] [ ] [ ] [ ] The corresponding augmented matrix will be: [ ] Using rref function: [ ] Which if we translate it back we get the only solution is: and
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Problem 4. The set of four vectors ( ) ( ) ( ) and ( ) are independent iff the following equation has only one solution (which is the trivial one): [ ] [ ] [ ] [ ] [ ] The corresponding augmented matrix will be: [ ] Using rref function: [ ] Which if we translate it back we get the only solution is: and Based on this reduced form matrix, and the set of new equations, it means that is a free variable in another word this system has many solution (pick any value for
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