Applied Mathematics 1411A/B Lecture Notes - Lecture 7: Elementary Matrix, Row And Column Vectors, Linear Combination
12 Mar 2015
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Recall: last class, we began studying several properties of determinants. Theorem (cramer"s rule): if that is a system of n equations in n unknowns such bx a. , then the system has a unique solution. A det( x where ja is matrix obtained by replacing the entries in the jth column of a by the entries in the column vector b b. Example: use cramer"s rule to solve the 2x2 system: x y. Example: use cramer"s rule to find the value of. 3 nn matrix, then the following statements are ni. A det( is consistent for every column vector b has exactly one solution for every column vector b. 0 has only the trivial solution: a is invertible, the homogeneous system, the reduced row-echelon from of a is, a is expressible as a product of elementary matrices. Application: a first look at eigenvalues and eigenvectors. This is a brief intro to what we"ll study in chapter 5.
