Solved Problems on Linear Algebra - Review Sheet | MATH 215, Study notes of Linear Algebra

Download Solved Problems on Linear Algebra - Review Sheet | MATH 215 and more Study notes Linear Algebra in PDF only on Docsity!

| a) LPs oeht ee Bare nxn matics and G is invertible , then det (GIAB™) = det A : ajcab? A— 0. tprmaosigaf | oe-ap He eigenvalues of A 1s tere £) Similor matices have tha same & valued 9) Simi lor matrices have the Same. Tach: herent e viana va are eigenve chor of a matix A, then they ore tinearly | indlepenclent . G Find the values porbishick det [: -l 2| <0 x= Misetig f cy Ad) tet matix has thee lea O ‘ , -dh we ER ie es. ne Eee is dim | and another ‘Ss 3-dim. s/t possible that fre matix is cot cliagonoliza ble ? Explain cart fully, '(@) Determine with measonss whether An~G. If An~6b ot an Inver fhle matnix s.¢ pla P5B2; = Poh: ne ac De [3 2 af let A= ‘ k S| ied all values of k pr which : values 3 anol ~I. luce wth alg. rmultip. 2 pe & U a) A has eigen b) A has an — c) A has 7° rea | ep relies K Jot 75 be the set of all order pons of real num bers (oe) Define (xaiyr d+ (x2, 42) = C341 t 342 pairks) G Cx Yr ) = b3e4h a | Show that S with these. operations jn n° whrch axioms fail te hole. Jet Wi and Wa be subspaue of Ras Shemp det MAGEE TO, RIO fico Och Ponbeee: subspae of 23. 8) fa vectr space j Shak exphii ty