# Math Portfolio - SL type 1 - matrix binomials

Math Portfolio SL Type 1:

Matrix Binomials

This portfolio deals with the investigation of matrix binomials. This portfolio will cover the basic knowledge of matrix in order to explain the methods and the procedure of arriving at the general statement. The task was to deduce a general formula for given matrices and to determine scope and/or limitation of this general statement. The general statement was obtained by using an algebraic method. All matrix equations were typed using the program MathType. It will test the validity of the general statement using GDC (GDC-TI-83). The scope and limitations of this general statement will also be discussed in this investigation.

Matrix is “a rectangular array of numbers arranged into a fixed number of rows (horizontal) and columns (vertical).” Each number in the array or the collection of numbers is called an element or entry of the matrix. The order of elements of the matrix is: .

Matrix has dimension of m (rows) x n (columns). The numbers m and n are the dimensions of the matrix and it plays significant role in the calculation of the matrix. For instance, the dimension of the following matrix is (2X2) since it has two rows and two columns:. For the addition of the matrices, corresponding elements need to be added. For example, If A and B were two different matrices but with the same dimensions, each elements are added according to its position of the matrix or the order of the elements. To add these two matrices, elements according to its order or position will be added; however, it needs to be remembered that this will only work when both matrices have same dimensions.

Example,

Scalar (real number) multiplication is the multiplication of the matrix using real number. In this case, a real number is multiplied by each element in the matrix one by one.

Example:

The multiplication of matrices is very different from the addition or the scalar multiplication of matrices. In the case of addition and the scalar multiplication, elements in the matrices had to be either added or multiplied according to their corresponding elements; however, this rule does not apply for the multiplication of matrices. It is based on row-by-column multiplication. For the multiplication of matrices, multiply the first element in the row by first element in the column. Then multiply the second element in the row by the second element in the column. This continues and in the last stage, products are added; however, this method only works when rows and columns have the same number of elements.

Example:

So, when both matrices A and B are multiplied, their rows and columns should have the same number of elements. For instance, the number of elements in the row of the matrix A should be equal to the number of elements in the column of the matrix B. Knowing the dimensions of matrices is useful for the multiplication of matrices.

Numbers in ‘n’ should be equal and numbers in ‘m’ and ‘p’ give the dimension of AB.

Example:

Since numbers in each column and in each row of ...