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. 1s along the diagonal and 0s 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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Lecture-6(matrix) - Any row or column has all elements...

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