# Precalculus: Chapter 7: Systems and Matrices

Last updated 5 years ago

Discipline:
Math
Subject:
Pre-Calculus
11

Precalculus Chapter 7: Systems and Matrices

VocabularySolution of a System- an ordered pair of real numbers that satisfies all of the equations or inequalities in the systemSolved the system of equations-to find all solutions of a systemSolve by Elimination- methods for solving systems of linear equationsSupply Curve- p=f(x); where x represents production and p represents priceDemand Curve- p=g(x); where x represents the range value of a functionEquilibrium Point (price)- a point where the supply curve and demand curve intersectm x n matrix- a rectangular array of m rows and n columns of real numberselement (entry)- any of the real numbers in a matrixorder of a matrix- m x nscalars-a real numberzero matrix-a matrix consisting entirely of zeros additive inverse-The opposite of b, or -bproduct AB- the matrix in which each entry is obtained by multiplying entries of a row of A by the correspoinding entries of a column of B and then addingtranspose-The matrix A^T obtained by interchanging the rows and columns of Amultiplicative identity- a square matrix with 1s in the main diagonal and 0s elsewhereinverse-the inverse of a square matrix A, if it exists, is a matrix B, such that AB-BA=I, where I=identity matrixnonsingular-a square matrix with nonzero determinantsingular-a square matrix with zero determinantdeterminant-a number that is associated with a square matrixGaussian elimination-a method of solving a system of n linear equations in n unknownsequivalent-systems of equations that have the same solutiontriangular form-a special form for a system of linear equations that facilitates finding the solutionaugumented matrix-a matrix that represents a system of equationscoefficient matrix-a matrix whose elements are the coefficients in a system of linear equationsreduced row echelon form-a matrix in row echelon form with every column that has a leading 1 having 0s in all other positionspartial fraction and decomposition-the process of expanding a fraction into a sum of fractions.solution of an inequality-a value of the variale for which the inequality is truesolved the inequality-to find all solutions of the inequalitygraph of an inequality-the set of all points in the coordinate plane corresponding to the solution of the inequalityhalf-plane-the graph of the linear equalityboundary-the set of points onthe "edge" of a regionobjective function(linear programming problem)-a method of solving certain problems involving maximizing or minimizing a function of two variables subject to restrictionsfeasible xy-points that satisfy the constraints in a objective function

Helpful WebsitesUsing the Subsitution Method Adding, Subtracting, Multiplying, and Dividing MatricesGaussian EliminationPartial Fraction Decomposition

Matrices are used to represent real-world data such as the habits, or traits of a population of people.

Real World Applications

Two variable inequalities can help businesses find maximum and minimum costs

Finding the Inverse of a Matrix

Partial Fraction Decomposition

Did You Know?The history of matrices goes back to ancient times! But the term "matrix" was not applied to the concept until 1850. "Matrix" is the Latin word for womb, and it retains that sense in English. It can also mean more generally any place in which something is formed or produced.