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Lecture18 - Matrix Inverse Matrix division is undefined...

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Matrix Inverse Matrix division is undefined However, there is a matrix inverse for non-singular square matrices
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= 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 a a a a a a a a a a a a a a a a A 44 43 42 41 34 33 32 31 24 23 22 21 14 13 12 11 = 44 43 42 41 34 33 32 31 24 23 22 21 14 13 12 11 a a a a a a a a a a a a a a a a A Augmentation Whatever you do to left-hand-side, do to the right- hand side (useful when solving system of equations)
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[ ] = 4 44 43 42 41 3 34 33 32 31 2 24 23 22 21 1 14 13 12 11 b a a a a b a a a a b a a a a b a a a a b A Augmented Matrix 4 4 44 3 43 2 42 1 41 3 4 34 3 33 2 32 1 31 2 4 24 3 23 2 22 1 21 1 4 14 3 13 2 12 1 11 b x a x a x a x a b x a x a x a x a b x a x a x a x a b x a x a x a x a = + + + = + + + = + + + = + + +
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MATLAB Matrix Manipulations >> A = [1 5 3 -4; 2 5 6 -1; 3 4 -2 5; -1 3 2 6] A = 1 5 3 -4 2 5 6 -1 3 4 -2 5 -1 3 2 6 >> A' ans = 1 2 3 -1 5 5 4 3 3 6 -2 2 -4 -1 5 6 Create a matrix Matrix transpose
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MATLAB Matrix Manipulations >> x = [5 1 -2 3]; >> y = [2 -1 4 2]; >> z = [3 -2 1 -5]; >> B = [x; y; x; z] B = 5 1 -2 3 2 -1 4 2 5 1 -2 3 3 -2 1 -5 >> C = A + B C = 6 6 1 -1 4 4 10 1 8 5 -4 8 2 1 3 1 >> C = C – B ( = A) C = 1 5 3 -4 2 5 6 -1 3 4 -2 5 -1 3 2 6 Matrix Concatenation Addition and Subtraction
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MATLAB Matrix Manipulations A = 1 5 3 -4 2 5 6 -1 3 4 -2 5 -1 3 2 6 B = 5 1 -2 3 2 -1 4 2 5 1 -2 3 3 -2 1 -5 >> A*B ans = 18 7 8 42 47 5 3 39 28 -13 19 -14 29 -14 16 -21 >> A.*B ans = 5 5 -6 -12 4 -5 24 -2 15 4 4 15 -3 -6 2 -30 Matrix multiplication and element-by-element operation A*B A*B A.*B A.*B
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MATLAB Matrix Manipulations >> D = [2 4 3 1; 3 -5 1 2; 1 -1 3 2] D = 2 4 3 1 3 -5 1 2 1 -1 3 2 >> A*D ??? Error using ==> * Inner matrix dimensions must agree.
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