3. [10 marks Matrix Multiplication - Part 1 In linear algebra, a matriz is a rectangular grid of numbers. Its dimensions are specified by its number of rows and of columns. This assignment and Assignment 4 focus on the representation and manipulation of square matrices, i.e., where the number of rows equals the number of columns equals n E.g., This is a square matrix where n-4: A+4 A+5 A+6 A+7 A2 A21 A22 A23 Ao As As2 Ass -2 0 7 3 A +12 A+13 A+14 A+ 15 Observe that the notation Aj refers to the matrix entry at the ith row and the jth column of A. Also observe that each row is laid out like an array in C, with increasing index by column. That's how matrices are stored in main memory: the elements from row 0 are followed by the elements from row 1, followed by row 2, and so on. Thus, the array has n2 elements, and the base pointer A, contains the address of the first element of the matrix, i.e., the oth element of row 0 Because of the regular pattern, entry lookup is random access, where the address of Aj equals A + L(i-n + j), where L is the size of each matrix element. For example, when L-1, as it is for this assignment, then the entry As2 can be found at address A +3.4+2 A+ 14. Matrir Multiplication: Boo Bo Bo2 Bos Cio C C12 Cis A10 A1 A12A13 A2o A2 A22 A2s Aso A31 A32 A33 B20 B21 B22 B23 C30 Csi C32 C33 ' 42 2,310 Let A and B be two n x n m atrices. Then their product AB is the n n matrix C, where the entry Cij is the result of the dot product of the ith row of A with the jth column of B For example, the value C32 is the dot product of row 3 of A and column 2 of B, highlighted in bold. The dot product of two arrays is resolved by multiplying their 0th coordinates, then their 1st coordinates, 2nd coordinates, and so on, and then taking the sum of their products. Explicitly, More generally, Ci,-2 Aik-Bkj. which leads ourselves to the algorithm. 3. [10 marks Matrix Multiplication - Part 1 In linear algebra, a matriz is a rectangular grid of numbers. Its dimensions are specified by its number of rows and of columns. This assignment and Assignment 4 focus on the representation and manipulation of square matrices, i.e., where the number of rows equals the number of columns equals n E.g., This is a square matrix where n-4: A+4 A+5 A+6 A+7 A2 A21 A22 A23 Ao As As2 Ass -2 0 7 3 A +12 A+13 A+14 A+ 15 Observe that the notation Aj refers to the matrix entry at the ith row and the jth column of A. Also observe that each row is laid out like an array in C, with increasing index by column. That's how matrices are stored in main memory: the elements from row 0 are followed by the elements from row 1, followed by row 2, and so on. Thus, the array has n2 elements, and the base pointer A, contains the address of the first element of the matrix, i.e., the oth element of row 0 Because of the regular pattern, entry lookup is random access, where the address of Aj equals A + L(i-n + j), where L is the size of each matrix element. For example, when L-1, as it is for this assignment, then the entry As2 can be found at address A +3.4+2 A+ 14. Matrir Multiplication: Boo Bo Bo2 Bos Cio C C12 Cis A10 A1 A12A13 A2o A2 A22 A2s Aso A31 A32 A33 B20 B21 B22 B23 C30 Csi C32 C33 ' 42 2,310 Let A and B be two n x n m atrices. Then their product AB is the n n matrix C, where the entry Cij is the result of the dot product of the ith row of A with the jth column of B For example, the value C32 is the dot product of row 3 of A and column 2 of B, highlighted in bold. The dot product of two arrays is resolved by multiplying their 0th coordinates, then their 1st coordinates, 2nd coordinates, and so on, and then taking the sum of their products. Explicitly, More generally, Ci,-2 Aik-Bkj. which leads ourselves to the algorithm