MATH 220 Midterm: Math 220 Midterm review
Document Summary
Inconsistent linear equation: if there is no solution. Matrix: information of a linear equation written in a rectangular array. (cid:1876)(cid:2869) (cid:884)(cid:1876)(cid:2870)+(cid:1876)(cid:2871)=(cid:882) (cid:884)(cid:1876)(cid:2870) 8(cid:1876)(cid:2871)=8 (cid:887)(cid:1876)(cid:2869) (cid:887)(cid:1876)(cid:2871)=(cid:883)(cid:882) We describe this matrix by its rows and columns. You can solve a linear system by eliminating different terms in the matrix. Elementary row operations: replace one row by the sum of itself and a multiple of another row. Interchange two rows: multiply all entries in a row by a non-zero constant. The starred entries may have any value (including zero). The squares also show the pivot position of the matrix: reduced echelon form: leadi(cid:374)g e(cid:374)t(cid:396)ies a(cid:396)e o(cid:374)e a(cid:374)d the(cid:396)e a(cid:396)e 0"s (cid:271)elow a(cid:374)d above each leading 1. Free variables: we can choose any value for this variable. When(cid:1876)(cid:2871)=(cid:882),the solution is (cid:4666)(cid:883),(cid:886),(cid:882)(cid:4667) when(cid:1876)(cid:2871)=(cid:883) ,the solution is(cid:4666)(cid:888),(cid:885),(cid:883)(cid:4667). each different choice of (cid:1876)(cid:2871) determines a (different) solution of the system, and every solution of the system is determined by a choice of(cid:1876)(cid:2871).
