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Recitation 03 Presentation

Recitation 03 Presentation - 14:440:127 Introduction to...

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14:440:127 Introduction to Computers for Engineers Recitation 3
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14:440:127 Recitation 3 Ways of selecting elements in a Matrix using colon (:) operator z = [ 7 2 6 3 ] [ 2 5 3 2 ] [ 3 6 4 2 ] z(:,2:3) % all rows, columns 2 through 3 ans = [ 2 6 ] Rutgers University SOE [ 5 3 ] [ 6 4 ] v = z(:) % turn z into a vector v = [ 7 2 3 2 5 6 6 3 4 3 2 2]
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14:440:127 Recitation 3 Some more examples using Colon operator z = [ 7 2 6 3 ; 2 5 3 2 ; 3 6 4 2 ]; z(2,[1 3:4]) % row 2, columns 1 and 3 through 4 ans = [ 2 3 2 ] end is a special variable referring to the last row or last Rutgers University SOE column z(2:end,end) % 2nd through last row, last column ans = [ 2 ] [ 2 ] z(end,[1 3:4]) % last row, columns 1 and 3 through 4 ans = [ 3 4 2 ]
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14:440:127 Recitation 3 Element by element math operations in Matlab Operands (vectors / matrices) must be of same dimension (same number of rows and columns) . Addition: a = [ 7 2 ; 6 3 ]; b = [ 1 3 ; 1 5 ]; a + b Rutgers University SOE ans = [ 8 5 ] [ 7 8 ] Subtraction: a - b ans = [ 6 -1 ] [ 5 -2 ]
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14:440:127 Recitation 3 Multiplication Dot Multiplication Multiplies ‘element by element’. Syntax ‘ .* Example Rutgers University SOE a = [ 7 2 ; 6 3 ]; b = [ 1 3 ; 1 5 ]; a .* b ans = [ 7 6 ] [ 6 15 ]
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14:440:127 Recitation 3 Matrix Multiplication: Inner dimension of the matrices must be equal. (i.e. the no of columns of the 1st matrix must be equal to the no of rows of the 2nd matrix) Dot product: a = [a1 a2 a3] b = [b1 b2 b3] dot product = (a1*b1)+(a2*b2)+(a3*b3) Rutgers University SOE The result is a Scalar. Dot product is different from dot multiplication. Cross product: a = [a1 a2 a3] b = [b1 b2 b3] Result = (a2*b3-b2*a3)i + (a3*b1-a1*b3)j + (a1*b2-a2*b1)k The result is a vector.
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14:440:127 Recitation 3 Examples of Matrix multiplication Matrix Multiplication: a = [ 7 2 ; 6 3 ]; b = [ 1 3 ; 1 5 ]; a * b ans = [ 9 31 ] [ 9 33 ] Dot Product: Rutgers University SOE a = [ 7 2 3 ]; b = [ 1 3 5 ]; dot(a,b) ans = 28 Cross Product: cross(a,b) ans = [ 1 -32 19 ]
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14:440:127 Recitation 3 Built in Matlab functions for vectors & matrices Sum : Vector, it adds individual elements of the vector.
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