Homework Sol Due 9-12-2011

# Homework Sol Due 9-12-2011 - ISEN 620 Homework Solutions...

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ISEN 620 Homework Solutions Due 9-12-2011 Consider the matrix A : 1 3 0 2 1 1 3 9 2 A = 1. Using the following ERO what is the result on A ? 1 2 2 1 3 3 2 3 Row Row Row Row Row Row + + 1 3 0 1 3 0 2 1 1 0 7 1 3 9 2 0 0 2 ERO ⎯⎯⎯→ 2. Using the result from 1, continue with ERO’s, what is the resultant A’ ? 2 2 3 3 1/ 7 1/ 2 Row Row Row Row 1 3 0 1 3 0 1 3 0 2 1 1 0 7 1 0 1 1/ 7 3 9 2 0 0 2 0 0 1 ERO ERO ⎯⎯⎯→ ⎯⎯⎯→ 3. Assume that we have the system of equations ( ) , 4 0 10 T Ax b b = = . Apply the following ERO’s to solve this system. What is the solution? 1 2 2 1 3 3 2 2 3 3 2 3 1/ 7 1/ 2 Row Row Row Row Row Row Row Row Row Row + + Applied to A we get the matrix answer of problem 2 above. Applied to the rhs ( ) 4 8 / 7 1 T b = , and using backward substitution we obtain ( ) 1 1 1 T x = .

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4. Using the augmented matrix approach with ERO’s to obtain the inverse of A : 1 2 2 1 3 3 2 2 3 3 1 3 0 1 0 0 2 1 1 0 1 0 3 9 2 0 0 1 using ERO's of 2 and -3 1 3 0 1 0 0 0 7 1 2 1 0 0 0 2 3 0 1 using ERO's of 1/7
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