Unformatted text preview: A1 , Z C1 ,and Y ZBA1 C 1BA1. A B X
b. 0 I 0 Y
0 Z I 0 0 I 0 0 I W e have
AX B0 I ,0 X I 0 0, AY B0 0,0Y I 0 0, AZ BI 0,and 0Z I I I , so
AX I , AY 0, and AZ B. W e conclude that X A1 , Y 0,and Z A1B. c. I 0 0 I A I 0 X B C I Y 0
I
Z 0 I 0 0
0 0 I 0 I 0 0 I O mitting the obvious relations, W e have
AI IX 0, BI CX IY 0,and B0 CI IZ 0, so
A X 0, B CX Y 0, and C Z 0. W e conclude that
X A, Z C,and Y B CX CA B. 3
6 1
4 1 , x 2 . C ompute:
2 . L et u , v , w 2
6 5 3 2
2
2
a. w w 3 ( 1) ( 5) 35.
b. x w 6 3 ( 2) ( 1) 3 ( 5) 5. c. x w 5 1 .
w w 35 7 d. 1
1...
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 Spring '08
 PAVLOVIC
 Linear Algebra, Matrices, Formulas, Dot Product, Euclidean vector, Inner product space, block matrix dimensions

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