Matrices

Matrix A matrix is an ordered rectangular array of numbers. The entry in the i th row and j th column is denoted by a ij. Ex. 4 Columns 3 Rows Size = Row x Column = 3 x 4

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. y + 1 = 4 and = 7 y = 3 and x = 14 Corresponding entries are equal

Addition and Subtraction of Matrices If A and B are two matrices of the same size, then 1.The sum A + B is found by adding corresponding entries in the two matrices. 2.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 – If A is an m x n matrix with elements a ij, then the transpose of A is the n x m matrix A T with elements a ji. Transpose of a Matrix Ex

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 matrixfind 5A.

 #1 P all, 9 – 19odd, 21 – 24 all, all