Unformatted text preview: L52a34— Q.,_ MA M 17mm Quiz 3. Last Name: First Name: 1. (4 marks) The matrix operations appearing in the following statements are always
deﬁned. Indicate whether the statements are always True or sometimes False: 7) If A is invertible, then AX = 0 has oo—many solutions True 7/ False
(77) (AT)T = A 3/ True False
(777) If A, B are symmetric, then so is AB True 7/ False
(772) AAT is a symmetric matrix, for any matrix A 3/ True False l
2. (2 marks) Given the system: AX = 0 , ﬁnd the solution, knowing that
—l
0 l l
A71 — l 2 2
0 2 3
q l o \ l l "
XZA [Q]: XLL'L’XRQ : ’l
“ — l o L '5 , ~3 3. (4 marks) Find conditions (if necessary) on 51,1)2,b3 such that the following system
is consistent: a: —— 3y — Z 2 b1
232—771—2252
2.72 —— 5y — 32 2 b3.
\ 3 —\ lo,
1 7 —\ b,_
2 s —s 53
l. 3 'l b1
\ l 2535,
O T—\ '—l ~Zb\+b3
l '5 "l b\
o \ \ .LerOL
0 O o «LtgprzLbs Fol THE s7sTEM Tq 8'6 Cossmeur we new ‘—L\l91"_\01+l03:0 \ ...
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 Spring '09
 MihaiBeligan
 Linear Algebra, Algebra

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