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Chapter 5: Systems of Equations and Matrices
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Terms in this set (26)
System of equation
(n) - Composed of two or more equations considered simultaneously
System of two linear equations in two variables
(n) - Ex: x - y =5 and 2x + y = 1
Solution of the system of equations
(n) - (Solving graphically) Each point at which the graphs intersect
Inconsistent system of equations
(n) - The system of equations has no solution
Consistent system of equations
(n) - The system of equations has at least one solution
Independent system of equations
(n) - The system of equations has a definite number of solutions
Dependent system of equations
(n) -The system of two equations in two variables has an infinite number of solutions
Equal matrices
(n) - Matrices have the same order and corresponding entries are equal
Opposite of a matrix
(n) - (also know as additive inverse) a matrix obtained by replacing each entry with its opposite
Zero matrix
(n) - A matrix having 0's for all its entries
Additive identity of a matrix
(n) - When the zero matrix is added to a second matrix, the second matrix is unchanged
Scalar Product
(n) - The scalar product of a number k and a matrix A is the matrix denoted kA, obtained by multiplying each entry of A by the number k. The number k is called a scalar
Row matrix
(n) - Matrix only consists of a single row
Column matrix
(n) - Matrix only consists of a single column, a matrix with only one column
Properties of matrix multiplication
(n) - For matrices A,B and C, assuming that the indicated operations are possible:
A(BC) = (AB)C: Associative property of multiplication
A(B+C) = AB + AC: Distributive property
(B+C)A = BA +CA: Distributive property
Important note: Multiplication of matrices is generally NOT commutative
Inverse of a square matrix A
(n) - A n
n matrix A-1 which A-1
A = I = A*A-1. NOT every matrix has an inverse
Invertible matrix
(n) - (also known as nonsingular matrix) The matrix has an inverse. Otherwise, it is singular matrix
Matrix solutions of System of equations
(n) - (for system of n linear equations in n variables) X = A-1B if A is an invertible matrix where X is the n*1 matrix of variables, A is the matrix of coefficients and B is the matrix of constants on the right sides of the equations
Minor of an element in a SQUARE matrix
(n) - (For a matrix A = [aij]) The determinant of the matrix formed by deleting the ith rom and jth column of the origin matrix. Denoted as Mij
Cofactor of an element of a matrix
(n) (For a square matrix A = [aij]) Aij = (-1)^(i+j)*Mij where Mij is the minor of aij
Determinant of Any SQUARE matrix
(n) - (For any square matrix A of order n*n (n>1)) Choose any row or column. Multiply each element in that row or column by its cofactor and ADD the results. The value of a determinant will be the same no matter which row or column is chosen. Denoted as |A|
Determinant of 1*1 matrix
(n) - The determinant is simply the element of the matrix
Linear inequality in two variables
(n) - An inequality that can be written in the form Ax+By < C, where A,B,C are real numbers and A and B are not both zero. The symbol < may be replaced with < ≤ ≥
Solution set of an inequality
(n) - All ordered pairs that make the inequality true
System of linear inequalities in two variables
(n) - A system consists of two or more inequalities in two variables considered simultaneously
Solution of a system inequalities
(n) - An ordered pair that is a solution of each inequality in the system
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