2.5 Coordinate Matrix

# 2.5 Coordinate Matrix - 2.5 2.5 The change of Coordinate...

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2.5. 2.5. The change of Coordinate Matrix 1. (a) F ([ x 0 j ] β ) (b) T (Since Q = [ I V ] β β 0 , Q is an isomorphism) (c) T (d) F ( B = Q - 1 AQ ) (e) T ([ T ] γ = Q - 1 [ T ] β Q ) 2. Q = [ I V ] β β 0 (a) I V ( a 1 ,a 2 ) = ( a 1 ,a 2 ) = a 1 e 1 + a 2 e 2 I V ( b 1 ,b 2 ) = ( b 1 ,b 2 ) = b 1 e 1 + b 2 e 2 Q = ± a 1 b 1 a 2 b 2 (b) Q = ± 4 1 2 3 (c) Q = ± 3 - 1 5 - 2 (d) Q = ± 2 - 1 5 4 3. Q = [ I V ] β β 0 (a) I V ( a 2 x 2 + a 1 x + a 0 ) = a 2 x 2 + a 1 x + a 0 I V ( b 2 x 2 + b 1 x + b 0 ) = b 2 x 2 + b 1 x + b 0 I V ( c 2 x 2 + c 1 x + c 0 ) = c 2 x 2 + c 1 x + c 0 116 PNU-MATH

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2.5. Q = a 2 b 2 c 2 a 1 b 1 c 1 a 0 b 0 c 0 (b) Q = a 0 b 0 c 0 a 1 b 1 c 1 a 2 b 2 c 2 (c) Q = 0 - 1 0 1 0 0 - 3 1 1 (d) Q = 2 1 1 3 - 2 1 - 1 3 1 (e) Q = 5 - 6 3 0 4 - 1 3 - 1 2 (f) Q = - 2 1 2 3 4 1 - 1 5 2 4. [ T ] β 0 = Q - 1 [ T ] β Q Q = ± 1 1 1 2 , [ T ] β = ± 2 1 1 - 3 [ T ] β 0 = ± 2 - 1 - 1 1 ¶ ± 2 1 1 - 3 ¶± 1 1 1 2 = ± 8 13 - 5 - 9 5. [ T ] β 0 = Q - 1 [ T ] β Q Q = ± 1 1 1 - 1 , [ T ] β = ± 0 1 0 0 [ T ] β 0 = 1 / 2 ± 1 1 1 - 1 ¶ ± 0 1 0 0 ¶± 1 1 1 - 1 = 1 / 2 ± 1 - 1 1 - 1 117 PNU-MATH
2.5. 6. [

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## This note was uploaded on 02/14/2012 for the course MAS 4105 taught by Professor Rudyak during the Spring '09 term at University of Florida.

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2.5 Coordinate Matrix - 2.5 2.5 The change of Coordinate...

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