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3e - L52a34— Q MA M 17mm Quiz 3 Last Name First Name 1(4...

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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 «Ltgprz-Lbs Fol THE s7sTEM Tq 8'6 Cossmeur we new ‘—L\l91"_\01+l03:0 \ ...
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