1. Sections 2.4 and 2.5 Matrix Operations
Chapter 2
Sections 2.4 and 2.5
Matrix Operations

2. Matrices
DEFINITION
A matrix is a rectangular array of numbers. The number in the array are called the elements of the matrix. The array is enclosed with brackets.
An array composed of a single row of numbers is called a row matrix.
An array composed of a singe column of numbers is called a column matrix.
The location of each element in a matrix is described by the row and column in which it lies. Count the rows from the top of the matrix and the columns from the left.

3. Example For the matrix Find the following: The (1,1) element (a11)
The location of –4
The location of 0
SOLUTION
2 is the (1,1) element. It is in the first row and first column.
4 is the (2,5) element. It is in the second row and fifth column.
–8 is the (3,3) element. (a33= –8 )
–4 is in the (2,4) location. (a24= –4)
0 is in the (1,5) location. (a15= 0)

4. Matrix Operations EQUAL MATRICES
Two matrices of the same size are equal matrices if and only if their corresponding components are equal. Matrices are the same size if they have the same dimensions.
EXAMPLE
Find the value of x such that
SOLUTION
Recall, for the matrices to be equal, the corresponding components must be equal. Thus, 4x = 9 or x = 9/4.

5. Matrix Addition
The sum of two matrices of the same size is obtained by adding corresponding elements. If two matrices are not the same size, they cannot be added; we say that their sum does not exist. Subtraction is performed on matrices of the same size by subtracting corresponding elements.
EXAMPLE
Determine the sums A + B and B + C for the following matrices.
SOLUTION
A + C and B + C do not exist.

7. Scalar Multiplication
Scalar multiplication is the operation of multiplying a matrix by a number (scalar). Each entry in the matrix is multiplied by the scalar.
EXAMPLE
Multiply the following matrix by –3,
SOLUTION

9. Multiplication of Matrices
Given matrices A and B, to find AB = C (matrix multiplication):
Check the number of columns of A and the number of rows of B. If they are equal, the product is possible. If they are not equal, no product is possible.
The number of rows in C is the same as the number of rows in A. The number of columns in C is the same as the number of columns in B.
Note: It is not necessarily true that AB will equal BA. The order of multiplication does matter.

10. Example Find the product AB of the two matrices given below: SOLUTION
To multiply the two matrices we need compute the corresponding dot products.

12. Homework P. 142 ([3 – 42]x3, 51, 60) P. 158 9-16 all 9/2/14 date