fm3_chapter31 - UN-20E A 1 B C D E F G H I MATRICES IN...

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Unformatted text preview: UN-20E A 1 B C D E F G H I MATRICES IN EXCEL Matrix A (a row vector) Matrix B (square 3 x 3 matrix) Matrix C (column vector) 13 -8 -3 2 3 4 5 6 7 8 9 10 11 2 3 4 13 -8 -3 -8 10 -1 -3 -1 11 Matrix D (a 4 x 3 matrix) 13 -8 -3 -8 10 -1 -3 -1 11 0 13 3 A 1 B C D E MULTIPLYING A MATRIX BY A SCALAR 6 2 Scalar 3 13 4 Matrix B -8 5 -3 6 7 8 Scalar * Matrix B 78 9 -48 10 -18 11 -8 10 -1 -48 60 -6 -3 -1 11 -18 -6 66 #MACRO? A 1 2 3 4 5 6 7 Matrix A 1 3 6 5 7 B C D E Matrix B 0.1 0 23 0 8 -33.4 -15 0 2.33 1.2 F G Sum of A + B 1.1 26 14 -10 9.33 H ADDITION OF MATRICES 3 0 -9 11 12 3 0 -42.4 11 13.2 I RICES 1 2 3 4 5 6 7 #MACRO? A 1 2 3 4 5 6 7 8 Matrix E 1 0 16 B C D E F G H TRANSPOSITION OF MATRICES 2 3 7 3 77 7 4 -9 2 Transpose of E: ET 1 0 2 3 3 77 4 -9 16 7 7 2 Cells F3:H6 are generated with the array function Transpose(A3:D5). This function is inserted by marking off the target area, typing the formula, and then finishing by pressing [Ctrl]+[Shift]+[Enter] . See Chapter 35 for more details. I TRICES 1 2 3 4 5 6 7 #MACRO? his function is inserted by marking off the target 8 ter] . See Chapter 35 for more details. A 1 2 3 4 5 6 7 8 Matrix A 2 0 B C D E Matrix B 9 2 F MULTIPLYING MATRICES -7 3 -52 12 6 -5 ### -12 4 Product AB 47 4 -15 6 1 2 3 4 5 6 7 8 MATRIX MULTIPLICATION: Number of columns of first matrix must equal Matrix A 2 0 A B C D E F number of rows of second matrix Can't multiply matrix B times matrix A! -7 3 Err:502 Err:502 6 -5 ### Matrix B 9 2 -12 4 Product BA Err:502 Err:502 Err:502 Err:502 A 1 2 3 4 5 6 7 8 9 10 11 12 13 1 0 0 0 1 3 2 5 B C D E F G H MATRIX INVERSE Use array function Minverse to compute the inverse of a square matrix Matrix A -9 3 4 7 16 2 0 3 1 3 -2 4 -0.0217 0.0000 0.0652 -0.0217 Inverse of A 1.8913 0.5362 -1.0000 -0.1667 -0.6739 -0.1087 -0.1087 -0.2971 Verifying the inverse #MACRO? 0 1 0 0 0 0 1 0 0 0 0 1 I J E inverse of a square matrix Inverse of A 2 3 4 5 6 7 8 9 10 11 12 13 -1.1449 0.6667 0.4348 0.1884 #MACRO? 1 A 1 2 3 4 5 6 7 8 9 10 11 12 13 1.0000 0.0000 0.0000 0.0000 1 3 2 5 B C D E F G H MATRIX INVERSE Use array function Minverse to compute the inverse of a square matrix Matrix A -9 3 4 7 16 2 0 3 1 3 -2 4 -0.0217 0.0000 0.0652 -0.0217 Inverse of A 1.8913 0.5362 -1.0000 -0.1667 -0.6739 -0.1087 -0.1087 -0.2971 Verifying the inverse #MACRO? 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 1.0000 I J E inverse of a square matrix Inverse of A 2 3 4 5 6 7 8 9 10 11 12 13 -1.1449 0.6667 0.4348 0.1884 #MACRO? 1 A 1 2 B C D E Column vector y 16 77 12 F G Solution A-1 Y 0.4343 -2.3223 0.3634 SOLVING SIMULTANEOUS EQUATIONS Matrix A of coefficients 3 4 66 3 0 -33 1 4 42 3 2 5 6 7 Checking that the solution works 16 8 77 ### 9 12 10 H NEOUS 1 EQUATIONS 2 3 4 5 6 7 8 9 10 #MACRO? ...
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This note was uploaded on 01/23/2011 for the course FGB 780 taught by Professor Edwardchang during the Spring '09 term at Missouri State University-Springfield.

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