# Pitt MATH 0280 - 0280Exam1Sol (6 pages)

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## 0280Exam1Sol

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## 0280Exam1Sol

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Pages:
6
School:
University of Pittsburgh
Course:
Math 0280 - Intro to Matrices & Linear Alg
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Math 0280 Exam 1 October 6 2AL4 Dr Thomas Everest a Soi nLr ong Il l I f Name S ot 46 s Instructions No caulculators phones or other technology allowed To receive full credit you must ju stify yotrr work If I cannot read or understand your work you witt not ea rn many points for that problern If you need more space for a probl ffi use the back of the p ge 1 10 points Let u 1 3 3J u Find 3u a u 2v 3 L Lf u e 8V w fi v v l 2 4 5 ffid rv o t a f l s 3 f lt t z uoJ 5 z il b Find the length of u v f LA v r ll n vll t l 1 il6 Find the value of a that makes the vectors v and w orthogonal r V4w r 4 7rn Lf t 5a 3 V vrf O if Y d Find the angle between u a rrd v CcSS f V lf ut ll llvll qh Leave your answer in the form cos 0 tLl NG t t rt J ts 1 F Ar 2 10 points Show that Ax b where x F I b r r I lo 4 o j qFFr lo r o o l o cj L o R ii z f t c r 4 o oo I t D o t x A t t S f il 4 I r I o o Lo I I t I R t o l r t 5 q f F t s4 f O I lD 3 tl t I L lJ ol tL Rr tR I and to L J f t s qlr f Lo 54 f il is invertible and use A Lto solve the system 0 c 7 t L0 o lf lj r 4L l t t Ksrz z s j rl I 3 l o I Io o q I r c e I A t 1l t AT q t l I Fl B I ol rDI D j t t dl 3 10 points Are Ll Lil rinearry independenr or dependent E If they are dependent find a specific linear combination that produces the z e r o vector Duab Ax s D h ve n o nLn v o 9o Lrt Y1 tt3 E Yg It ts Ls z i RsrR f I sz oo D Tr ca fL t l j a I y5 Tu 1 8 fl 7 o h J Y AA t V C 3V 4 10 points A BC u Find A F fl B l il ffid e l l B r L 3 l l D 7 ABC if I I l fr Fr Iz L 1 l o L D I o FZ I I 1o O q b Give an example of two matrics A AB BA fto and B such that AB and BA both exist but Ctn 5 vK S A 6 3 AB rj il ftB f BA ol B bJ i 1 Lt t f o i Lo j BA fo L il 5 5 points The vectors u the form ar l zKs l Ir lo bu W cz l 7l 0 1 7tt l and v are non parallel Find an equation of jt that represents the span of u and v in IR3 B It Dl Lt v3 3 D o yls g 3 I S aZ t F IE 3 X F 3 v 7V I Lvt sist e t l g I Z Lo To 7l wlLr r a 32 zx 3 t3L O BONUS 6 3 points bomrs Shoriy that matrix if A is a quare matrix then A A is a syrnmetric BT SqY ff1 LrtL f B J B n r t Ar Ar t Ar A A Ar ArAt t N Ar s syw n trrL Ar A o 7 4 points bonus Show that for u and v in R v 1 u rrl l ltU rll llou will receive no credit if you ttse specific vectors L q L4 tA v llt ll rA vl I L q ll j v h v o L l n d wr zL v n u d f t L L It I F HFv I bt r J L t e v LT L4 G V j zr ev F t l

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