MATH125 Lecture Notes - Lecture 17: Transpose

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

Document Summary

Every linear system a11x1 + a12x2 + . + a1nxn = b1 a21x1 + a22x2 + . + a2nxn = b2 am1x1 + am2x2 + . + amnxn = bm can be written in the matrix form ax = b where a = (aij) is the coe cient matrix, x is the column vector of variables x1, . , xn and b is the column vector of constant terms b1, . [ a | b ] for the augmented matrix of a linear system is just shorthand for the matrix equation ax = b. Combining this observation with our previous results we see that ax = b has a solution if and only if b is a linear combination of the columns of a. There is another useful fact about matrix multiplication: multipli- cation of a matrix a by a standard vector can be used to pick up a column or a row of a.