CHE
Matrix Manipulation on Excel

# Matrix Manipulation on Excel - 11.1 a 1 3 2 11.2 c A= 1 2 3...

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Bryan (Daejin) Kim CHE141L 10/13/2006 11.1 a) A= B= X= 1 -2 3 17 X1 3 1 -2 0 X2 2 3 1 7 X3 11.2 c) A= B= 1 4 5 6 2 C= 3 A*B = C 4 5 6 8 10 12 12 15 18 11.4 A= B= 6 0 -3 5 -5 -7 -1 4 9 0 9 2 8 -5 2 4 -1 0 a. A+B=C 11 -5 -10 b.B+A=C 11 -5 -10 -1 13 11 -1 13 11 12 -6 2 12 -6 2 c. A-B=C 1 5 4 d.2A=C 12 0 -6 -1 -5 7 -2 8 18 4 -4 2 16 -10 4 e. AB=C 18 -27 -42 f. BA=C -21 15 -74 31 32 15 7 26 85 48 -87 -66 25 -4 -21 yes, a. and b. are equivalent. However, e. and f. are not equivalent because in addition, the order doesn't matter, but in multiplication, the two matrices have different numbers in their own rows and columns 11.6 A(11.1)= A inverse 1 -2 3 0.17 0.26 0.02 3 1 -2 -0.17 -0.12 0.26 2 3 1 0.17 -0.17 0.17 A(inverse) * A

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1 0 0 0 1 0 0 0 1 A(11.5)= A inverse 6 0 -3 0.13 0.04 0.03 -1 4 9 0.19 0.09 -0.13 8 -5 2 -0.07 0.08 0.06 A(inverse) * A 1 0 0 0 1 0 0 0 1 A* A(inverse) 11.1 A*A(inverse) 11.5 1 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 yes, A*A-1 = A-1*A 11.8 A= X= B 4 -2 1 X1 6 1 3 -7 X2 34 -2 0 -5 X3 14 A*X = B A(inverse) 0.16 0.11 -0.12 -0.21 0.2 -0.32 -0.07 -0.04 -0.15 A(inverse) * A * X = B * A(inverse) X1 0.16 0.11 -0.12 6 X2 = -0.21 0.2 -0.32 * 34 X3 -0.07 -0.04 -0.15 14 = 3 x1 = 3
1 x2 = 1 -4 x3 = -4 11.10. A B a. 1 2 7 8 9 10 3 4 11 12 13 14 5 6 C 29 32 65 72 b. A B 1 2 3 4 5 C= 32 6 c. A B= 4 5 6 1 C= 2 4 5 6 3 8 10 12 12 15 18 d. A B 1 2 3 5 4 5 6 -3 7 8 9 2 C 5 17 29 11.15 a. A X B 1 -2 3 X1 17 3 1 -2 X2 0 2 3 1 X3 7

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A-1 0.17 0.26 0.02 X1 3 -0.17 -0.12 0.26 X2 = -1 0.17 -0.17 0.17 X3 4 b. A X B 0.1 -0.5 0 1 X1 2.7 0.5 -2.5 1 -0.4 X2 -4.7 1 0.2 -0.1 0.4 X3 3.6 0.2 0.4 -0.2 0 X4 1.2 A-1 -0.22 0.22 0.77 0.71 X1 2 -1.05 -0.95 1.69 -5.57 X2 = 1 -2.33 -1.67 4.15 -15.43 X3 -2 0.49 -0.49 0.77 -2.86 X4 3 c. A X B 11 3 0 1 2 X1 51 0 4 2 0 1 X2 15 3 2 7 1 0 X3 15 4 0 4 10 1 X4 20 2 5 1 3 13 X5 92 A -1 0.09 -0.07 0.03 -0.01 -0.01 0.03 0.31 -0.09 0.02 -0.03 -0.04

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• Fall '06
• caenepeel
• Bryan, 0.3 cm, 0.5cm, 0.2 cm, 0.03cal

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