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Linear Algebra BS Mathematics 6 Semester/Term BZU — Bahauddin Zakariya University 2021

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Ayesha Mustafa· 1 day ago

BS ZOOLOGY first semester Animal diversity ZOOL 101 - university of Punjab 2025

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Abubakar· 1 day ago

Literary criticism

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Guest· 2 days ago

this paper consists of 60 marks but now we have 35 marks paper.

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Annie· 2 days ago

Can you please tell me more past papers please because my exams are starting from next week

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Ahmed· 6 days ago

Did you provide the past papers of the science of society uos?

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Paper text

B5-636-21-25 PRESS COPY BAHAUDDIN ZAKARIYA UNIVERSITY, MULTAN Examination: Final- Term Course Title: Unear Algebra and its Application Maximum Marks: 60 Note: Attempts All Questions. BS Mathematics Course Cade: Math-304 Semester: 6* Session: 2021-25 Time Allowed 2 | hours. Sr.# 1 Questions (a) Prove that is the smallest subspace of V containing S. Marks 2 (b) Let 5 = (61,€3,53) wherc 6) = (1,0,0), cz= (0,1,0),€y = (0,0,1). Show that S is Basis forR (p) Find the Basis from the column space of -3 -25 Am 一6 9 -1 2 -6 9 -1 9 7 －1 -11 2 -5 一4 (b) State and prove Rank-Nullity Theorem. (a) Let T:V → W be a linear map. If [FP. ., Pn J spans V then 06 4 5 (b) Consider the following two basis of?. S= （ty,12）= （（1.2），（3,5））and S'- ［0u, 1） = （（1，-1），（1，-2）） Find the change of basis matrix P from & to the new basis S'. (a) Find the Eigen values and Eigen vectors of given matrix 1 11 -1 2J (b) State and Prove Chachy Schwarz inequality. (a) Apply the Gram Schmidt algorithm to transfer the basis V; = (1,1,0,1), ½ = (1,0,1,1), V⅓ = (0,1,1,1) Into orthogonal basis. (b) Let 4 = 7 3] then find an orthogonal matrix P S.t D = p-IAP is a (6) Let = [3 diagonal. 06 06 OG 06