Mathematics 1229A/B Lecture 20: Lecture 20

• School: Western University
• Department: Mathematics
• Course: Mathematics 1229A/B
• Professor: Mohsen Mollahajiaghaei

Document Summary

Theorem x y 2 0 y 2 0. 2y 12 0 x y 142 0 be 1 homogeneous b non homogeneous. Remark thezerovector o is a solution ofeveryhomogenous linearsystem thesolutionx 0 iscalledthetrivialsolution ofthe homogenoussystemanyothersolution iscalled a non trivial one solutions t yeo. Rank the rank of a matrix a isthenumberofnon zero rowsinthenewreducedechelonform of a example findtherank of ra ar lo i r o. Example findtherankof it a it it iiiit iiiit. Rankandthenumberofsolutions thehomogenouslinearsystem ax o where a is a mxn matrix has g l c. A mi n l auniquesolution thetrivialone if therankof a n. Let axe 0 bea linearsystem where a is a 4 6 matrix whichone is true aboutthe ofsolutions unknowns he equations. 2 solutions a solutions dependsontherankofa equations l ofunknowns. Theorem consider thesystemaxeb wherea is an m x n matrix let p bethe rank ofa andlet q betherank of alb thenax b has.