PGE 310 - HW 2 - Solution(1)

PGE 310 - HW 2 - Solution(1) - The University of Texas at...

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The University of Texas at Austin Fall 2011 - PGE 310: Formulation and Solution in Geosystems Engineering Homework #2: Linear Algebra – Precision and Error Calculation - Working with Pseudocodes By Hossein Roodi 1. Linear Algebra (BY HAND) Given the matrices, vectors and scalars below, answer/calculate the following.  4 3 1 2 u 3 2 1 5 v   4 5 2 1 w T x 2 1 2 1 1 2 3 2 1 1 5 2 A 1 2 2 4 2 1 2 3 1 B 4 2 Scalar and B and A or x w and v u Dimensions T : ) 3 3 ( : ) 1 3 ( ) 3 1 ( : ) 4 1 ( : , : a) u w v u a T T T  ) ) (( ) 4 1 ( : 4 1 )] 1 4 ( ) 4 4 [( )] 1 4 ( )) 4 1 )( 1 4 [(( ] ) 4 1 ( )) 4 1 ( ) 4 1 [(( : ) ) (( : u w v u Dimensions Checking T T T T T T T T 4 1 1 4 4 4 1 4 4 1 1 4 36 27 9 18 36 27 9 18 ) 4 5 2 1 12 8 4 20 9 6 3 15 3 2 1 5 6 4 2 10 ( ) 4 5 2 1 ) 3 2 1 5 4 3 1 2 (( : ) ) (( : T T T T T w v u n Calculatio   4 1 32 24 8 16 4 3 1 2 ) 2 )( 4 ( : u 4 3 1 2 ) ) (( u w v u a T T T b) x A B b T ) ( ) 1 3 ( ) 1 3 )( 3 3 ( )] 1 3 ( )) 3 3 ( ) 3 3 [(( : ) ( : T T x A B Dimensions Checking 11 7 1 2 1 2 13 19 2 7 21 0 2 9 3 2 1 2 ) 1 1 2 3 2 1 1 5 2 1 4 2 2 2 3 2 1 1 ( 2 1 2 ) 1 1 2 3 2 1 1 5 2 1 2 2 4 2 1 2 3 1 ( ) ( : T T x A B b n Calculatio T
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c) ) ( ) ( x B x c T ) 1 1 ( )] 1 3 ( )) 3 3 )( 3 1 [(( )] 1 3 ( )) 3 3 ( ) 1 3 [(( : ) ( ) ( : T T x B x Dimensions Checking  36 4 2 4 10 12 7 ) 2 1 2 2 )( 1 2 2 4 2 1 2 3 1 2 1 2 ( ) ( ) ( : x B x c n Calculatio T d) Calculate the 1 L , 2 L and L norms of v .
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PGE 310 - HW 2 - Solution(1) - The University of Texas at...

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