22Amidterm2sol

22Amidterm2sol - Name (1 point): Schweim 22A Midterm 2 1 0...

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Unformatted text preview: Name (1 point): Schweim 22A Midterm 2 1 0 0 2 2 0 1. (15 points) Suppose M = 3 —1 0 0 1 2 . Solve the system 0 0 201 _1 we 46% mm, Lbs—ax, W» L: K; 3 0% LO\ H1010 MX=V,whereV=( fl“, 59%;“ TS W : L t 2. SUN—“3131’ % VOL: Lt ‘50 W0: 1w\ +4115: :=> (/35' -5 We, ‘Hruw Sc\Wr UX= W/ w‘wb U; o O'\ W 50%;“ is —)(3-.; —3 :5 stg M: \00 1L0 '3 \oo\2~.\)=(7,\ (— 3' ' *~ =1 .,-’ D '1 2. (isfhim (313‘ L3 \ / 1 2. (15 points) Only one of the following matrices is invertible. Figure out which one, and for the one that is invertible, calculate its inverse. 102 ’102 002 3—16 3_16 3_16 000 010 010 m (-23: :0 we 2r in as (m 5; my; 00 ’ll/WUQW, 1+ CS vwlr \ 0 (MC (go'lg\: 14'“ + 1kg: 0 5° l '3 Mg \kalcle, 3. (25 points) (a) (5 points) Define the determinant of an n X 71 matrix M (permutation definition). (b) (8 points) Prove that, for an n x 72 matrix M , det kM = k" detM for any real number k. (c) (12 points) Suppose det JV! 2 3 and det N = 2.F0r each of the follow- ing, either say what the determinant is or if the determinant cannot be determined from the information given. 1. detMN 2 ii. detMTN“1 = iii. det(M+N-1) 2 iv. det N4 = a) an M "2', mm mawmtm 6. w . bi Ore M" 5% M = (8me (MAM, we, w, (tic \«M v M U8th -~~(>I‘Lem\ = Act (do; 1.1 we Jmt M = View, W ems" MW e 26: $8453 win.» reg» ' \«MQ—w .: i semen \«(T New "New 0" z k“ E $3455 “\Gm ~ ~ 6m 6‘ . : \‘K‘A [Oi—Uh M a} u out Me: b H) M MTN": 5/2. * at.) M- m M" We a... Wimfi m M N“ 2“ >15 3 4. (12 points) Answer true or false for each statement. (a) (3 points) Given 121,1»; in a vector space V, span{v1, 122} is always a .bs I ace. False (b) (3 points) An suare matrix has an inverse. True (c) (3 points) 41 ' invertible if and only if M X = 0 has no solutions. True w (d) 3 oin‘t_‘s_)mToday is Monday. ~ True False 5. (5 points) What is the adjoint of M = 6. (17 points) (a) (3 points) Define what it means for a set {121,112, . . . ,vk} of vectors to be linearly independent. 2 4 ——1 (b) (7 points) Are the vectors { (—1) , (1) , < 1 J } linearly indepen- 0 1 1 dent? Explain your answer. 1 (c) (7 points) Determine the value of a for which (a) lies in the span 1 1 —2 —2 5 ,L 5 gm (V .15) a (ll 4° L“ “ “It ave/W 33“ -3$ , ‘ “1C -\- S5 $42.in V'LS ’\ ~1¢+Ss=\ ' sow w w be we" (:23 w e 7. (10 points) Calculate the product: ...
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This note was uploaded on 03/23/2010 for the course MAT 022A taught by Professor Pon during the Spring '10 term at UC Davis.

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22Amidterm2sol - Name (1 point): Schweim 22A Midterm 2 1 0...

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