Section 2.4 Matrices

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

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

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.

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

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. 1 4 7 2 5 8 3 6 9

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.