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Lecture-6(matrix) - – Any row or column has all elements...

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Matrix Operations (II) Lecture - 6
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Matrix Multiplication =$B$3*J2+$C$3*J3+$D$3*J4
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Matrix Multiplication Matrix multiplication can be easily performed using array math operations Select 2 X 4 area, and type function: =MMULT(A,B) PRESS CTRL+SHIFT+ENTER Array named A Array named B
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Matrix Multiplication =MMULT(B2:D3,G2:J4) Try to make a change to the formula Press X to get out of this error What is the problem with these?
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Transpose of a matrix Transpose is - Interchanging rows and columns Copy to clipboard Select Transpose
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Matrix Transpose Array function Transpose can also be calculated as an array operation PRESS CTRL+SHIFT+ENTER
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Determinant =1*C22-3*G22+5*K22 + - + - + - + - + Sign convention for calculating the determinant Can you calculate the determinant taking Column 2 as the basis?
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Determinant EXCEL built-in function MDETERM(xx) Can you calculate the determinant of: 1) 2) 3) 13 5 7 0 0 0 12 9 7 13 5 13 11 13 11 12 9 12 13 5 14 11 13 -32 12 9 -9
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Some things to remember .... The value of the determinant will be zero if:
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Unformatted text preview: – Any row or column has all elements identically zero – Any two rows or columns are identical – Any row or column can be expressed as linear combination of two or more rows or columns of the matrix Inverse of a matrix • Given a matrix A , the inverse of that matrix is a matrix C such that: I is a identity matrix - i.e. 1’s along the diagonal and 0’s everywhere else C is designated as A-1 Several methods for calculating inverse exist: – Gauss Jordan elimination – Gaussian elimination I C A = ⋅ Matrix Inversion For a 2 x 2 matrix A-1 = = For a 3 x 3 matrix Matrix Inversion • Looking at the expressions on previous slide - it is going to be a problem if det{ A } = | A | = 0 If det{A} = 0 , then matrix A is termed singular Inverse cannot be computed . Array operation, press CTRL+SHIFT+ENTER =MMULT(B3:D5,G3:I5) Subject to round-off error...
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