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Quiz+16+solution

# Quiz+16+solution - MATH 17100 28446 Quiz 16 solution 11/16...

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MATH 17100 28446 Quiz 16 solution 11/16/ 2009 1. Find the rank of the coefficient matrix as well as that of the augmented matrix associated with the given systems of equations. Then solve the system of equations and express the solution as a vector: (a) 3 2 0 2 1 2 4 x y z x y z x y z + = + = =− Augmented matrix, [ ] 3 1 2 0 1 2 1 4 1 0 1 2 1 0 1 0 | 2 1 1 1 0 3 3 9 0 1 1 3 0 1 1 0 1 2 1 4 0 5 5 1 2 0 0 0 3 0 0 0 1 =− A b ( ) 2, ( ) 3 rank rank = = A A | b from the number of non-zero rows in the echelon form. ( ) ( ) System is inconsistent and no solution exists rank rank A A | b (b) 3 9 6 3 2 2 6 4 y z y z y z = + = + = Augmented matrix, [ ] 3 9 6 1 3 2 1 3 2 | 1 3 2 1 3 2 0 0 0 2 6
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