MATH136 Chapter Notes - Chapter 45-50: Linear Combination, Free Variables And Bound Variables, Elementary Matrix

• School: University of Waterloo
• Department: Mathematics
• Course: MATH136
• Professor: Dan Wolczuk

Document Summary

An equation in n variables (unknowns) x1, . , xn that can be written in the form a1x1 + + anxn = b (1) where a1, . , an, b are constants is called a linear equation. The constants ai are called the coe cients of the equation and b is called the right-hand side. A set of m linear equations in that same variables x1, . , xn is called a system of m linear equations in n variables. If a system of linear equations has at least one solution, then it is said to be consistent. , then ~x = ~s + c(~s ~t) is a distinct solution. Two systems of equations which have the same solution set are said to be equivalent. The augmented matrix of the system is a11 a12 a21 a22 am1 am2 a1n a2n amn b1 b2 bm.