1. Section 2.4
Matrices

2. Matrix
A matrix is an ordered rectangular array of numbers. The entry in the ith row and jth column is denoted by aij.
Ex.
3 Rows
Size = Row x Column
= 3 x 4
4 Columns

3. Square matrix – same number of rows as columns.
Ex. Here is a 2 x 2 matrix:
Two matrices are equal if they have the same size and their corresponding entries are equal.
Ex. Find x and y.
Corresponding entries are equal
y + 1 = 4 and x/2 = 7
y = 3 and x = 14

4. Addition and Subtraction of Matrices
If A and B are two matrices of the same size, then
The sum A + B is found by adding corresponding entries in the two matrices.
The difference A – B is found by subtracting the corresponding entries in B and A.
Also, we have the Commutative law: A + B = B + A and Associative law (A + B) + C = A + (B + C) for addition.

5. Ex. Given matrices A and B, find A + B and A – B.

6. Transpose of a Matrix
Transpose of a Matrix – If A is an m x n matrix with elements aij, then the transpose of A is the n x m matrix AT with elements aji.
Ex.

7. Scalar Product – If A is a matrix and c is a real number, then the scalar product cA is the matrix obtained by multiplying each entry of A by c.
Ex. Given the matrix
find 5A.