examen parcial 2021 GTIAE, Exámenes de Álgebra

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UPC. ETSEIB. GETIAE. Algebra and Geometry. Partial exam, 30 October 2019. Time: 1h 15”. Family name: First name: Grade: 1. Find the sum of all the possible products of two different A complex) br roots 0£ 7. Fa ad, esta e) 1272 ¿0 : Y e 0 da e y Ug > e 7 241, Uya UF. IA E ON - UA, UL . 44, Uy, UFI o e gn A 2. A polynomial pla) has degree at most 3, and complies that n23=1, pQ)=0 pB)=1) p(8)=-1 Find p(x) and its roots. pOx) > ax? elry* ecxed y Plesta da lr ee p()> Barulrlced- / 2, Malal. palizas ebecz0 ¡ALE 1 1 12 US A IE TÍ AS Flo). bar lle, rl 4 Ad PAM roots tp e/ CA 00 Lo ya 3 % nn PA a gts 5.0089, 1005250 3. Find the rank of the matrix A, for every real value of the parameter a. 1.1.1 2 A 1 a -1 a-2 2 ( a+l 1 13)- 0 ar 0 3 1.0 -1 0 o A 0 Ta lo 10 2