Chapter 27

# Chapter 27 - UN-20E A B C 1 2 3 4 5 Matrix A(a row vector 2...

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Unformatted text preview: UN-20E A B C 1 2 3 4 5 Matrix A (a row vector) 2 3 4 6 7 8 9 10 Matrix D (a 4 x 3 matrix) 13 -8 -3 11 -8 10 -1 12 -3 -1 11 13 0 13 3 14 D E F G H I MATRICES IN EXCEL Matrix B (a square 3 x 3 matrix) 13 -8 -3 -8 10 -1 -3 -1 11 Matrix C (a column vector) 13 -8 -3 J A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 B C D E F G H I J K MATRIX OPERATIONS Multiplication by a scalar Scalar 6 Matrix B 13 -8 -3 -8 10 -1 78 -48 -18 -48 60 -6 -3 -1 11 Scalar * Matrix B -18 <-- =D7*\$B\$5 -6 66 Addition of matrices Matrix A 1 3 6 5 7 Matrix B 0.1 23 8 -15 2.33 3 0 -9 11 12 Sum of A + B 1.1 26 14 -10 9.33 0 0 -33.4 0 1.2 3 <-- =B20+E20 0 -42.4 11 13.2 Transposition of matrix Matrix E 1 0 16 2 3 7 3 88 7 Transpose of E = ET 1 0 2 3 3 88 4 -9 4 -9 2 Multiplication of matrices Matrix A 2 -9 Product AB 42 -69 -6 3 6 -75 6 -5 9 2 -12 4 -48 <--Array contains formula 120 =MMULT(A42:B43,D42:F43) Product BA -- this won't work Err:502 <-- =MMULT(D42:F43,A42:B43) 16 The framed area contains 7 the array function 7 =Transpose(A30:D32) . 2 To use this function: Mark off the whole area; put in the formula, then finish by pressing [Ctrl]+[Shift]+[Enter]. L A B C D E F 1 MATRIX INVERSE 2 Inverse of A: 3 Matrix A 1 -9 16 1 -0.0217 4 3 3 2 3 0.0000 5 2 4 0 -2 0.0652 6 5 7 3 4 -0.0217 7 8 9 Verifying the inverse 10 We multiply A*Inverse A: cells contain array function MMULT(A4:D7,F4:I7) 1 1.07E-015 -2.22045E-016 -9.4369E-016 11 0 1 -1.11022E-016 2.22045E-016 12 1 5.55112E-016 13 6.94E-018 8.33E-017 1 14 1.39E-017 1.17E-015 -4.44089E-016 G H I Array function Minverse(A4:D7) 1.8913 0.5362 -1.1449 -1.0000 -0.1667 0.6667 -0.6739 -0.1087 0.4348 -0.1087 -0.2971 0.1884 J A B C D E F G 1 SOLVING SIMULTANEOUS EQUATIONS 2 Column Solution 3 vector Y A-1 Y 4 Matrix A of coefficients 3 4 66 16 0.4343 5 0 -33 1 77 -2.3223 6 42 3 2 12 0.3634 7 8 9 =MMULT(MINVERSE(A5:C7),E5:E7) 10 11 12 Checking that the solution works 16 13 77 Contains the array function 14 12 =MMULT(A5:C7,G5:G7) 15 16 ...
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Chapter 27 - UN-20E A B C 1 2 3 4 5 Matrix A(a row vector 2...

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