Mathematics 1229A/B Final: Final Formula Sheet

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

Document Summary

Ily o b linearsystems are non homogenouswhen ax b b1 0 xx y t 2 1. Rank thenumberof non zerorows in row reducedechelonformof a. Rank of leading 1s to r i o. Auniquesolution trivialsolution infinitelymanysolutions if the rank of a s n if the rank of a n unknowns equations n solutions. For a system ax b let p be the rank of a and q bethe rankof ealb. No solution if p s g uniquesolution if p g i n infinite solutions if p q and p s n. Alb alsohas parameterfamily of solutions if theaugmentedmatrix then thesystemhas an ch r. For a system ax b withrank r rank r. If a is a nxn matrix thefollowingconditions are equivalent. 2 ax b has a uniquesolution for anyb. 5 the row reducedechelonform of a is 1 theidentitymatrix. Determinant for n 2 a cd bcc det e. For matrix a the submatrix aij isobtainedbydeleting the ithrowandj th column of a ithrow.