~ MAl31D1-~+-
MSSIGNMENli
r r r
111 +-
1
lltl: QUES ll!INS Fltll:tl-ANSWERED
lllUE: 15 JULY 2026 ------...+
DISCLAIMER:
- TRr,-DtlcUMENT I DR71EFERENCE ANO-SUT • E PURP SE
ONLY. I DD NDTt TAKE RESPbNSIBIUITY jFDR AN~ PLAGIARl~M. tMISUS . DR
ACADEMIC MISCONDUCT RESULTING FROM THEIR USE. IT IS YOUR j ~ ·
RESPDNSIBILIT T ENSU E ORIGINALITY AN~ CDMPLIAN E WITH
RELEVANT GUI ELINES DR STANDARDS. ~
, PLEASE USE THIS DOCUMENT AS A GUIDE ONLY
Question 1
(ll) Verification of -,1 and ]ts Eigrem1,a~ue 1
lo verify "f ,a vector • is an eigenvector of a matr~x A;.we look fa a sealar l. (the eigenvalue)
suci1 that t he matrb::-vector multnpllcat i:on satJs.fies the eharacte' istic equation:
A , -_ A\ .. ,
By mu tiiplyi ng the matrix A = ( 111 !) by the column vector 1 = ( ~1) . the resulting
vecio is t he zero vector;
o).-.
A :1 (
O'
Because a1ny 2ero vector can be expressed as a scalar mu tiple o t he original vec o where the
scalar is. :zerro. we,rewrite this as:
A ,1 == 0 ( 1)
-1
o Argument Since A .•1 yJelds.a perfect sea air mump e o . 1 , l is verified:as an ·e[genvector.
o Assooiated Eigenvalue· )q =0
MSSIGNMENli
r r r
111 +-
1
lltl: QUES ll!INS Fltll:tl-ANSWERED
lllUE: 15 JULY 2026 ------...+
DISCLAIMER:
- TRr,-DtlcUMENT I DR71EFERENCE ANO-SUT • E PURP SE
ONLY. I DD NDTt TAKE RESPbNSIBIUITY jFDR AN~ PLAGIARl~M. tMISUS . DR
ACADEMIC MISCONDUCT RESULTING FROM THEIR USE. IT IS YOUR j ~ ·
RESPDNSIBILIT T ENSU E ORIGINALITY AN~ CDMPLIAN E WITH
RELEVANT GUI ELINES DR STANDARDS. ~
, PLEASE USE THIS DOCUMENT AS A GUIDE ONLY
Question 1
(ll) Verification of -,1 and ]ts Eigrem1,a~ue 1
lo verify "f ,a vector • is an eigenvector of a matr~x A;.we look fa a sealar l. (the eigenvalue)
suci1 that t he matrb::-vector multnpllcat i:on satJs.fies the eharacte' istic equation:
A , -_ A\ .. ,
By mu tiiplyi ng the matrix A = ( 111 !) by the column vector 1 = ( ~1) . the resulting
vecio is t he zero vector;
o).-.
A :1 (
O'
Because a1ny 2ero vector can be expressed as a scalar mu tiple o t he original vec o where the
scalar is. :zerro. we,rewrite this as:
A ,1 == 0 ( 1)
-1
o Argument Since A .•1 yJelds.a perfect sea air mump e o . 1 , l is verified:as an ·e[genvector.
o Assooiated Eigenvalue· )q =0
