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wksht08

# wksht08 - MATH 152 L1 L2 Applied Linear Algebra and...

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MATH 152 L1 & L2 Applied Linear Algebra and Differential Equations Spring 2004-05 ¥ Week 08 Worksheet (March 21, 2005) : Matrix Q1. (Addition and scalar multiplication) Solve 3 A - 3 1 2 2 = - 3 2 4 - 2 . Q2. (Matrix multiplication) Simplify A [(3 A - 7 B ) - (7 A + 2 B )] - ( A - 2 B ) B . Q3. (Matrix equation) Let A = 1 y - y 2 x and B = x - 2 x y 2 . Find x , y such that BA = O . Q4. (Inverse) Verify that A = 0 0 1 0 1 2 1 2 3 and B = 1 - 2 1 - 2 1 0 1 0 0 are inverse to each other. Then compute the inverses of A 2 and A t . Q5. (Symmetric matrix) Show that if A is symmetric, then so are A - 1 and A t .

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Q6. (Augmented matrix) Write down the augmented matrix for the system of linear equations - x 2 +4 x 3 = 2 , x 1 +2 x 3 = 5 , 3 x 1 +2 x 2 = 1 . Q7. (Augmented matrix) Write down the system of linear equations with the following matrix as the
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wksht08 - MATH 152 L1 L2 Applied Linear Algebra and...

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