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Unformatted text preview: Click to edit Master subtitle style Engineering 101 Matrices and Linear Equations A programmer started to cuss Because getting to sleep was a fuss As he lay there in bed Looping 'round in his head while(!asleep()) {sheep++}; Quote of the Day Mahatma Gandhi Honest disagreement is often a good sign of progress. Matrices n One very important data structure for doing engineering and scientific computation is the matrix. n A matrix is a two dimensional array. n A matrix can be represented as a vector of vectors. 3 2 5 4 4 1 2  1 Matrices n We can think of labeling each element of the matrix by its row and column A11 A12 A13 A21 A22 A23 A31 A32 A33 Aij = Matrices n The numbers of rows and columns can be different from each other A11 A12 A13 A21 A22 A23 A31 A32 A33 Aij = Matrices and Vectors n Matrices and vectors can be multiplied by each other. To do this the number of columns in the matrix must equal the number of elements in the vector. A11 A12 A13 A21 A22 A23 A31 A32 A33 b1 b2 b3 b1 b2 b3 Matrices and Vectors n To perform the multiplication each row of the matrix is multiplied by the vector and all the results are added up. A11 A12 A13 A21 A22 A23 A31 A32 A33 = A11 b1 + A12 b2 + A1 3 b3 Matrices and Vectors n To perform the multiplication each row of the matrix is multiplied by the vector and all the results are added up. A11 A12 A13 A21 A22 A23 A31 A32 A33 = b1 b2 b3 A11 b1 + A12 b2 + A1 3 b3 A21 b1 + A22 b2 + A2 3 b3 Matrices and Vectors n To perform the multiplication each row of the matrix is multiplied by the vector and all the results are added up. A11 A12 A13 A21 A22 A23 A31 A32 A33 = b1 b2 b3 A11 b1 + A12 b2 + A1 3 b3 A21 b1 + A22 b2 + A2 3 b3 A31 b1 + A32 b2 + A3 3 b3 Matrices and Vectors n To perform the multiplication each row of the matrix is multiplied by the vector and all the results are added up. A11 A12 A13 A21 A22 A23 A31 A32 A33 = A11 b1 + A12 b2 + A1 3 b3 A21 b1 + A22 b2 + A2 3 b3 A31 b1 + A32 b2 + A3 3 b3 b1 b2 b3 Matrices and Vectors n To perform the multiplication each row of the matrix is multiplied by the vector and all the results are added up. 41 3 7 0 1 1 1 3 2 1 = 4* 3 + 0* 2 + (1)* 1 3* 3 + 7* 2 + 0 * 1 0* 3 + 1* 2 + 0* 1 1* 3 + 0* 2 + 1* 1 Matrices and Vectors n To perform the multiplication each row of the matrix is multiplied by the vector and all the results are added up....
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This note was uploaded on 04/07/2010 for the course ENGR engr 101 taught by Professor Rinenberg during the Spring '10 term at University of Michigan.
 Spring '10
 Rinenberg

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