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# Class Notes for Mathematical Sciences at Clemson University

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##### MATH-3110 Lecture 5: 5.2 the characteristic equation

L20 l 8 ( 52 Jnf cnrnClc r1trc ::A::J @ To fyn_ d 10 c .C~~e,~ v~ ~Af._~ Df o _~ o:-tY At we _ Yb ,~1<le.tr v,,~..,_vru_ t~v,_ ~ ~_r~ sv (-, 1no-r 0-I( t_ -?il ~~~ u ~ - - - - t ~ e C0. O i t-n~ ~ ~0 UVt )~ ,o A - ?.l - -~...

Mathematical Sciences
MATH-3110
Kevin James
##### MATH-3110 Lecture 4: 4.4 coordinate systems

L\IL\/\8 \ t\<.:,') 'y ~ 'I Unlq\~( \C'\ \J < C\ ( ~t ry r,C <:_ r-. rl (' ' t ? j ... . "(J< ...

Mathematical Sciences
MATH-3110
Kevin James
##### MATH-3110 Lecture Notes - Lecture 5: Codex Corbeiensis I

6. \- t\9En:iCA\\\es8 tJf1nve.ctDYs 1 1Le\nA,-oc an_ rixn ma r-Y,~-A no"'1:cvG vct~ v ~e-."' \sca\\c.on -eqen vc_tc:o< A \f tnev-et:i\~~- sorne&ca,ar /\ ER SJJ jtnif Ax...

Mathematical Sciences
MATH-3110
Kevin James
##### MATH-3110 Lecture 4: 4.5 the dimension of a vector space

J I C<t.-i~ ~mt V 0 0. v ec-()~ ~Cl(Ql A.1ir) os.~ B-= {lo, I b ..? ond. tt1T- ~ c_ V ., __ S~ n t YUY ~ ~ Yu < ,~CM=>D d... - . l Pt: !: ~n t ?~( QG t .,,l,~1 ~v I VJ_(1 [ v]fo }:vp-.~~ ~ w_ ~ 10 l:D-Slu .f>~ Tl 5:VQQ (_...

Mathematical Sciences
MATH-3110
Kevin James
##### MATH-3110 Lecture 5: 5.3 diagnolization

c>.r) ,.,(;, _-:JrlI . ~ -thcxt P ~ YJ( CD,e c~nci-no-r ~ =? J)~ - _____ C()P!~.JA- -fv (.-:::l , . , _ _ 2 2 1 A =-()D P- )(PD P )- PJ ( o -p) r.)t>-, ~ P _p __p-:_ I At:-:: p D, h p - - . . - - An f) Xf <fO..f, :..~o.Q ...

Mathematical Sciences
MATH-3110
Kevin James
##### MATH-3110 Lecture 4: 4.6 rank of a matrix

I i A ,.on rY)<ffl( f-Y)(J,-J~ V1 tj} !A 0. sa C Oe.tu()of yOUI~ rstoa G ( (CI) (((I : !@ fne S,er Cf (n~ ,h f r OV-.VCCtOv-~ r_ ~,,. vca, -cmr,e ~ o J,e(jl}( s9()<1 rv rRx.n .J..-1ronspose ---, [ta,,..ih)a, t ~ C wede nnc...

Mathematical Sciences
MATH-3110
Kevin James
##### MATH-3110 Lecture 4: 4.7 change of basis

- I -- -- - -i j -, I I

Mathematical Sciences
MATH-3110
Kevin James
##### MATH-3110 Lecture 2: 2.1 matrix operations

o.l , ai > a~ I o"',- C~\ j C\ t _.),...::,_l,, ~ ~ A -t 1:>= [a,, o.L .c,,~l,\_ b , \:,l . ~ [ a tb I) \ . L"'b]J. ... La Yi' "~ u. A -t~ -= b-\"A ...

Mathematical Sciences
MATH-3110
Kevin James
##### MATH-3110 Lecture Notes - Lecture 2: Fax, Intelligence Quotient

. - nv ~ T ~ R" -"rz~\" \\ nta V- l~C: ~ 1 \< \nv v\,n\<.:lf (l)Yc.vevq b e{R th ~t fY<JCt\yone x .~ .. 1\'YJti- <><) b No-\e: , ff'\\lSY)e..I-\ C\nQ 0\'110 ...

Mathematical Sciences
MATH-3110
Kevin James
##### MATH-3110 Lecture Notes - Lecture 4: Continuously Variable Transmission

---- -- ---- ----- --- ----- --- -- ---- -- -

Mathematical Sciences
MATH-3110
Kevin James
##### MATH-3110 Lecture 3: 3.2 properties of determinates

,~::::;...--Vtov,, ~ al ) J e.O c<v-, ~, h.lt ond ~ o.v( <YC~c~ QV1CnOii 2 oc n A :) rex,o, iJa <-n J , VC>(i) ,~ R O:~<r>-~.,Y,c(aM~A) ~ tt~) Q) I-{ ~ ?.l1 c--inercelA) de.-1lB) x t t .),~ ~ c ~ L nic., c.e-HA) t ce~l~) ...

Mathematical Sciences
MATH-3110
Kevin James
##### MATH-3110 Lecture 4: 4.2 null space column space and linear transformations

;>m rI. . l I..)l-J1~ 1l Sl.Q.LJ:~ (,C,JVIC r r -- - (). L ll.CQt f, or, 41 ~y <Y -t.lf1: . - 2.. ~ chl..: j , ~ c-vc mo r ,~ 0 c. ~y (.<_<: o i V (l CC c-:..0 t~ c V I} -- ( G~(0 l H ( (Y~( 0 ( , 2) r I .)<..( ( .rC ..(...

Mathematical Sciences
MATH-3110
Kevin James
##### MATH-3110 Lecture 4: 4.3 linear independence in vector spaces and bases

L~6 - LneoY- 1_v,c-e-p nec1er ,cc Y yecm Y ~ wc. e S ~ E a(,r <:, Qe.-nn 1 no ri- .. GS L e -V b e C. V (~:ii?( S..10CC O 11( r ,~- I. 1,.v~-J :.~:.;1 ~- v . .f: t-h<:<:1-> ~( ),. ) r ,(, tL Y, t ( Cll 0.19~ . ___ ___ ___ ...

Mathematical Sciences
MATH-3110
Kevin James
##### MATH-3110 Lecture 3: 3.1 determinants

6 D ete.Y-nYO(l t u C o~ bd f- -cd - -- - ------- a 0fJ~ CCL~(P.- Jfu-c- 0 0 u~ -be - ------- - ~ - fr--::ito, 1e_-co0 tae<rbi~-tcdhc_eq-a.rn-dbl*c.

Mathematical Sciences
MATH-3110
Kevin James
##### MATH-3110 Lecture 3: 3.3 Cramerâ€™s rule

I I Ser b ID ::~ - Cr:o.mec,.s P.I<:... iDe:ffll()0~--fuO.-A ~, 0.-,.0 ;J1sor, In x n mcx>Y, [-->< ...v,~->.<2.we~Q7:,k<~ I A i,lb)cca,, .o.,-,:oo L, ITo-c<:cm lcxo,cr,,v<.el : ..tna A 1.; 1 q() flXy, cY-oleYKAI).:=<0.u.l ...

Mathematical Sciences
MATH-3110
Kevin James
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