22Amidterm2sol

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

This preview shows pages 1–6. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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: ...
View Full Document

## 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.

### Page1 / 6

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

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online