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Elementary - Linear Algebra - Quiz Solution, Exercises of Linear Algebra

Eternal University Linear Algebra

This is the Quiz Solution of Linear Algebra. Mainly includes points are Explicit Conditionsm, Expansion Across, Equilibrium Prices, Equation, Elementary, Elementary Row etc. Key important points of tags are: Elementary, Determinant, Matrix, Intermediate, Results, Operations, Some Matrix, Multiplied, Added, Second Row

Typology: Exercises

2012/2013

Uploaded on 02/27/2013

sethuraman_h34rt 🇮🇳

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Math205B Quiz 06 page 1 11/06/2009 Name~

1. Find the determinant of the following matrix by hand, showing all your steps (intermediate results) along the way.

7

f

.. Z; ~O'~ Lp.JI f{,b mnIt/J!3. ~c;;dw t'*~ t:i'C/"ts(»'V 2)

/7.Jr;;"/./jf?''' ~cJ "

1~ ~ ~ we JU dfJ(g) =-'i

l!~ ;~I

=-'1(4/s:/+ 2 l

iD

.

5" /

" '310 I :J I

"

((~

)~,)

).vvj fl Co~r~~

,== -, 't ?O -l-t:t +2l'D.J-5'SV()cra~ f(JV :1../d!t/).l;<.]/J1J'r/x

,..:::: -if'7(-q) .~, ([jj)

4 -5 8 ~. l- 7

2. SupposeU= [0 3 4 ]= -'i~,-3' -10) ="1 fl - '((",)-.. '/<6l..(

007

Suppose the following elementary row operations turn some matrix Ainto U:

Step one: rows 1 and 3 of Aare swapped,

Step two: in the matrix resulting from step one, the second row is multiplied by 6

Step three: in the matrix that results from step two, twice the third row is added to the second row.

Find det(A) and show all your work.

Tf w~ label-k J ~i'I1~ Ptwfnc~ co/!rFd' ~ 4- ~'J« ao ~ ~, gS)

iI- ve'" Ide! Ej s£; 11 =u: 71~ tId(£; )/d:( £) oId(E;)U(/J) =' o/d:{v)

-.So ::L' r;, , -I .M (;;) ~'7-s-{ 0

yw~ "'-"" /'tOwC)1.I.f#C TV v ore P'~'/I EI£'l. R(;) J

bJ jvst}, CP4<-: ~~ V~0r- f/J~(/Jw.,./'clif: dd h

E, =[~~ ~J.E1.::f! ~gl. EJ -= f?~~7 J(J$rIt

.

f/l1~ jIA(m;/1 *~ ~k.

f ()f7) ,[; () I)) L~" iJ SDL\lJ/l/C( #;r ~(1) J tie l"ai

[

-59 84

]k(AI -'1'3#7- /y

3A.Findtheeigenvaluesofe= -42 60 ; showallyourwork. I{'J - -- (; == -I

t- Jw.~/lh~rd;.tc ~'

J1i(c-).I)-:::::

/

-stt- A gy

/-;::. (-SCJ- »(60->-)-(--'t~(glj)

-'12. ~O-A

,;:: -35'10 -A-+- ~z- T 3)"2 g>

~0~-VK;;~ j jm«;f Rjjhmkj C

~!j ~:1 Jeaf, vi ~~/;a151..

I

l

3B. One of your eigenvalues A should be positive. Find all the corre,'p(mding eigenvectors for this A. Verify that one of

them indeed satisfies ex =Ax (choose an easy x)" ..) II. J. .-LA ~f.. It,M II s;, A'

I./,'H, A::' Y, "'€ .wJ< ,JJ. X ~~ C~':::~)C'; 1Ii C()/~Uf/JYJj X~h JTA. IISCAt:ce. d

r~sq- .., ~'1 J=[

-(,3 g'-{]IV [I~~

]/e It xitV<-c&.J;nvltYkrj(1]]

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,(rt~~ dJtfl~ j" C[j]~t-;i 2~1[1]=[::J='1[l]ao~i>

Discover Exercises of Linear Algebra Eternal University

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Math205B Quiz 06 page 1 11/06/2009 Name~

Find the determinant of the following matrix by hand, showing all your steps (intermediate results) along the way.

f

/7.Jr;;"/./jf?''' ..^ Z;^ ~O'~~^ L^ p.JI f{,b^ mnIt/J !3.^ ~ cJ^ c;;dw^ t'*~^ t:i'C/"ts(»'V^ 2) "

1~ ~ ~ we JU dfJ(g) = - 'i

l

I

4 /

s : /

2

l

iD

.

5"

" '310 I :J I /

"

~ )

~ ,)

. vvj fl Co~r ~~

, == -, 't ?O -l-t:t + 2l'D.J - 5'S V ()cra~ f(JV :1../d!t/).l;<.]/J1J'r/x

, ..:::: - i

f '7 (-q)^ .~,

([jj)

4 -5 8 ~. l- 7

2. SupposeU=

[

]

007 = -'i~,-3'^ -10)^ ="1^ f^ l - '((",)-..^ '/^ <6l..(

Suppose the following elementary row operations turn some matrix A into U: Step one: rows 1 and 3 of A are swapped, Step two: in the matrix resulting from step one, the second row is multiplied by 6 Step three: in the matrix that results from step two, twice the third row is added to the second row. Find det(A) and show all your work.

Tf w~ label -k J ~i'I1~ Ptwfnc~ co/!rFd' ~ 4- ~'J« ao ~ ~, g S)

iI- ve'" Ide! Ej s £; 11 = u: 71~ tId( £; ) /d:( £) oId(E;)U(/J) =' o/d:{v)

-. So ::L' r;, , -I. M (;;) ~ '7-s-{ 0

yw~ "'-"" /'tOwC)1.I.f#C TV v ore P'~'/I E I £'l. R(;) J

bJ jvst}, CP4<- : ~~ V ~ 0r- f/J~(/Jw.,./'clif: dd h

E, = [~^ ~ ~J.^ E1.::f!^ ~gl.^ EJ^ -=^ f?^ ~^ ~7^ J(J$rIt

.

f/l1~ j IA (m;/1 *~ ~k.

f ()f7) , [; () I)) L~" iJ SDL\lJ/l/C( #;r ~(1) J tie l"ai

[

]

k (AI - '1'3#7- / y

3A. Findtheeigenvaluesof e = -42 60 ; showallyourwork. I{'J - - - (; == - I

t- Jw.~/lh~rd;.tc ~ '

J1i

c -). I ) -:::::

/

-stt - A gy

/

-'12. ~O-A^ (-SCJ-^ »(60->-) -^ (--'t~(glj)

, ;:: -35'10 - A -+- ~z- T 3)"2 g>

~ 0~-VK;;~ j jm«;f Rjjhmkj C

~ !j ~:1 J eaf, vi ~~/;a15 1..

l