HW8_14_sol

# HW8_14_sol - M 3 40L C S H omew ork Set 8 S olutions 1 F...

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M 340L CS Homework Set 8 Solutions 1. Find formulas for X , Y , and Z in terms of I , A , B , and C and inverses. Assume A , B , and C have inverses. (Hint: Compute the product on the left, and set it equal to the right side. First, pretend the blocks are simply real numbers but make sure you do not ever divide you may multiply by inverses, however. Be careful about right and left multiplication.) In all cases, assume the block matrix dimensions are such that the products are defined. a. 0 0 0 0 X A I Y Z B C I       We have 0 , 0, 0 0 0,and 0 , XA B I YA ZB X C Y ZC I so , , and . XA I YA ZB ZC I   We conclude that 1 1 1 1 1 ,Z C ,and . X A Y ZBA C BA     b. 0 0 0 0 0 0 0 A B X Y Z I I I I       We have 0 ,0 0 0, 0 0,0 0 0, 0,and0 , AX B I X I AY B Y I AZ BI Z I I I so , 0, and . AX I AY AZ B   We conclude that 1 1 ,Y 0,and . X A Z A B   c. 0 0 0 0 0 0 0 0 0 0 0 0

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