finall98spring

finall98spring - M a thL in ea rA lgeb ra :F in a lE xam in...

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Unformatted text preview: M a thL in ea rA lgeb ra :F in a lE xam in a t ion D ep to fM a th ,HKU ST ,Sp r ing N am e : T u to r : IDN o . S ec t ion : P rob lem N o .(p ts) N o .(p ts) N o .(p ts) N o .(p ts) N o .(p ts) T o ta l(p ts) S co re .C on s id erth e lin ea rtran s fo rm a t ion T : R ! R g iv enby T B B B @ x x x x C C C A = xx + x x + xx xx + xx x + x + xx : (a )W r iteth estanda rdm a tr ix A o fth e lin ea rtran s fo rm a t ion T .(po in ts) (b )F indba ses fo rN u l A ,R ow A andC o l A .(po in ts) (c )F inda llv ec to rs x x x x su ch tha t T B B B @ x x x x C C C A = .(po in ts) .L e t A = "# ; " # ; and "# . (a )W h ichon e iso rthogona llyd iagona lizab le?I fso ,ndano rthogona lm a tr ix Q su ch tha t Q ? AQ is d iagona l.(po in ts) (b )W h ichon e isd iagona lizab le? I fso ,ndam a tr ix S su ch tha t S ? A S isd iagona l.(po in ts) (c )W h ichon e isno td iagona lizab le? I fso ,ndam a tr ix P su ch tha t P ? A P iso fth e fo rm " ab ba # . (po in ts) .L e t A =. (a )Is A d iagona lizab le?le?...
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This note was uploaded on 01/28/2011 for the course MATH 113 taught by Professor Beifangchan during the Fall '08 term at HKUST.

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finall98spring - M a thL in ea rA lgeb ra :F in a lE xam in...

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