University:
University of Cambridge
Course:
0580 IGCSE | Mathematics
Academic year:

2024
Views:

369

Pages:

7
Author:

Pasti M

1. WEEK TO :3 2. SOFTWARE: Maple 13 3. NAME: Pasti Menang 4. OBJECTIVES: After following this module, students are expected to be able to perform operations on matrices such as addition, subtraction, multiplication and can determine other operations that can only be performed on matrices such as determinant, transpose, and matrix inverse. 5. INTRODUCTORY THEORYDefinition of Matrix A matrix is a set of numbers arranged in a rectangular shape based on the order of rows and columns. The numbers that make up the matrix are called elements. Matrices are expressed in the form mxn where m denotes rows and n denotes columns Example of a 3x3 ordered matrix A 2. Matrix Reduction Suppose there are two matrices, namely matrix A and matrix B. if matrix C is the subtraction matrix of A with B then matrix C can be obtained by subtracting each element in matrix A that is aligned with each element in Matrix B. therefore the requirement that two or more matrices can be subtracted is that they must have the same order. Matrix subtraction has the same properties as matrix addition. 3. Matrix Multiplication a. Matrix multiplication with scalars Suppose there is a matrix A of order m X n and a real number (scalar) that is k. the multiplication between matrix A and scalar k is denoted kA which is obtained by multiplying each element of matrix A by scalar k. all matrices of arbitrary order can be multiplied by a real number (scalar). b. Multiplication between matrices Suppose there are two matrices, namely matrix A with order mx p and matrix B with order p x n. The multiplication of matrices A and B is denoted A x B which is obtained from the sum of the product of the corresponding elements in the i-th row of matrix A with the j-th column in matrix B with i=1,2,3,... m and j = 1,2,3,...n. The requirement for two matrices to be multiplied is that the first matrix must have the same number of columns as the number of rows in the second matrix. The order of the matrix resulting from the multiplication of two matrices is the number of first rows times the number of second columns, for example the multiplication of a 2x3 matrix with a 3x2 matrix.