MATH125 Lecture 10: 10

• School: University of Alberta
• Department: Mathematics
• Course: MATH125
• Professor: Nikita

Document Summary

There are two important matrices associated with a linear system: the coe cient matrix and the augmented matrix. A general linear system of m equations in n variables x1, x2, . , xn can be written as a11x1 + a12x2 + + a1nxn = b1 a21x1 + a22x2 + + a2nxn = b2 am1x1 + am2x2 + + amnxn = bm. A matrix with m rows and n columns is said to have size m n. the number of rows is always written rst. Thus size of a matrix tells how many rows and columns it has. Consider a linear system (1) x1 2x2 + x3 = 9 and it has size 3 3. 9 | 9 and it has size 3 4. Note that if a variable is missing (as x1 in the second equa- tion) its coe cient 0 is entered in the appropriate position in the ma- trix.