Question

- 8. If A is an mxn matrix, What's the largest passible value for its rank and the smallest possible value for its nullity? 18.a) If A is a 3x5 matrix, then the rank of A is at moet - Why? b) If A is a 385 matrix, then the nullity of A is at most -. Why? c) If A is a 3x5 matrix, then the rank of AT is at most. Why? d) If Aisa 3x5 matrix, then the nullity of AT is at most - : Why?

Answer 1

Inderdhanush, Pego Inderdhoruch Agora DATE: DATE: 1 if A is a 3x5 Matrix, then ranKAT is almost LAT is 5X3 Matrix Sel! AT is 5x3 matrix then IiR GIRS then rank is atmost 3: Lif A is an mxn matrix what is the largest possible value o for its rank and the smallest possible for its Dullity? Salt Let A is an mxn matrix q We can txes for changer I matais to Linear Transform T:1R1RM O case if nem then By Banknullity theorem No 1 (0)- n then largest possible zonk Sloan then smallest INERTO _N() + nan N()=0) Gif A is 3x5 matrix, then NC) is atmost of AT, AT is 583 then T:1832 IRS + By dan K-Mullity - theorem B(A) +NLT) =3 , so if SCA) is zero phen Nilo is at most 3. to case a Tf mah then rank-hullity theorem NIT) F3 (1)-n e largest possible rank (1)= my then smallest allo) NIO+man nl (T) = n-m if A is 3x5 matrix, then ranks of A is atmost Il why Sell THRS IR by a IN(T+507)-5, then i gani of A is almost LS 3. Nality as A is atmosti By ganly- Alattity theorem Til min S(A) is o, then N(T) + 0 =5 CScanned with CamScanh.No=375 बेटीबचाओ बेटीपटाडो बेटी बचाओ बेटी