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Chapter 4

Matrices

QuestionAnswer
What is a matrix? A matrix is a rectangular arrangement of objects, each of which is called an element of the matrix. One use of matrices is to store data.
How are two matrices equal? Two matrices are equal matrices if and only if they have the same dimensions and their corresponding elements are equal.
What is the definition of matrix addition? If two matrices A and B have the same dimensions, their sum A + B is the matrix in which each element is the sum of the corresponding elements in A and B.
What is scalar multiplication? The product of a scalar k and a matrix A is the matrix kA in which each element is k times the corresponding element in A.
What is the definition of Matrix Multiplication? Suppose A is an m x n matrix and B is an n x p matrix. Then the product A X B(or AB)is the m x p matrix whose element in row i and column j is the product of row i of A and column j of B.
What is the definition of a matrices for size changes? For any k not equal to zero, the transformation that maps (s,y) onto (kx,ky) is called the size change with center (0,0) and magnitude k, and is denoted S sub k. S sub k (x,y)= (kx,ky)
What is the definition of matrices for scale changes? For any nonzero numbers a and b, the transformation that maps (x,y) onto (ax,by) is called the scale change with horizontal magnitude a and vertical magnitude b, and is denoted S sub a,b.
Created by: Southlawn