Math 205B Quiz 04 page 1 10/16/2009

Narne~I.SW SD~n..s

1.LH~[~; ~]andB~[:;]

(IA) Find the matrix product AB.

l,e ~a.tt-t-l.g

b.[ T ].~ -fS'.g-

;. J. +4- z.. .,. Z

Jt-rC+ lftt t/(P

10,7 .,. ~'1. ., s- - ~c.+S'L

2tt +Sl

110 +11 J

(IB) Suppose the :first two entries in the first row of this product are 0 and -1 respectively. Find c.

.so C-t 'ItA .,./(, =:D ..

a.nd 2t;.of" S=-I~2a.-::- C, =t a-=:-J ~ C.-fo'1{-l) +It. -=09' C-/2 +/(P :-Q

=>(+'f:() ~o

2. SupposeA= [: :].What is A-I? Under what conditions on m, n, s, t is A a singular matrix?

f) ~!fJ"/t.- /MM1!; I~A~

mt. -.In WB e7",1i101

fA/ kAa A-t tlPt't" ~-t &;elft~

/

-I

~]

J- f:. -V\ .

fJ - ~ t-~Y\-S)'VI ,f~/ttd /YIt -Sf) :f:0,

3. Suppose A is a 2x2 matrix which row-reduces to hafter the following row operations are applied in this order to A:

(step 1) Row 1 of A is replaced with (row 1 + 4 row 2). II ,dt I-DrO

J

-'{JJr IJ. Z. -0 I

(step 2) The second row of the resulting matrix is divided by 2.

(step 3) In the matrix resulting from step (2), the second row is replaood with (row 2 + 3 row 1).

(3A) WMt~t:~[Cj]-~:'~i([~ OO:~c;J 2@d 3, _M~'!

(3B) The produet of EI, E2, E3, in some order, gives A-I. What is that order'? (eg, "B2EIE3"?)

[JJJ} =I2. ~(!JJ, 1£i)

(3C) From ~~ what is A-I?

rUt, E, £ ,IJ £J;.;. ic..ktlf,.t;r ao />I.mk.I

[I-t] WJ~ [cJ(Y!Jrd'~ J ~'"(/J t,. 4 rnMi'I'xrt4

(3D) What.. A? Explain Jc][i\]fA] gi:iJ, /J-i -= [;,;.>]#4.: [A] tMfll [~i) ,HAl.

)

.ow you fmmd It (there iii/I I( f

:()1t-W~ . RI<EF([; ;,I~ ~]htlh [~~I ~Z 1 rore than one way 00 find it). TN. .A jtIuirJk.. .

) ~ Vk f~lM-z 4fop~: ([

.'Z'S ~'1 ], r.:;j I fJ (. (A .;r;:..4I~ f./J-

7) -@ ", ,( .. I./U-J... .J , . ~l"~-J,,-(.~ -2c;'',1- [~~~ [A J . tk /sTth.tr>.I/i-;.f.ft:.t.

,.,,.,,. «I..M.-, ~f., '" _Ir"(ic). ealtvlr.l1r}