MAT223H1 Study Guide - Midterm Guide: Linear Combination, Distributive Property, Augmented Matrix
Document Summary
Definition: a linear equation in variables/unknows 1,2, is an equation of form. Where 1, are called the coefficients of system. (1, ). Called constant term or right hand side: a solution to (*) are numbers 1 so that if 1 =1 =, then (*) is satisfied. Definition: a system of linear equations in unknowns 1, , is of the form. , = 1, , = 1, are called coefficients of system. , = 1, , are constant terms. Examples: is coefficient of in its equation: a solution to (**) are numbers 1, so that if 1 =1 = all equations in (**) are satisfied simultaneously. Goal is to find out if a system of linear equations has a solution and if it does, how to find all of the solutions. What can happen in general, a system of linear equations can have either a unique solution, no solution or infinitely many solutions.
