June 2014_final - CONCORDIA UNIVERSITY Department of...

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( CONCORDIA UNIVERSITY Department of Mathematics & Statistics Course Mr*hematics Number 204 Section(s) A Examination Final Date June 2014 Pages 2 Instructors S. Chowdhury Course Examiner E. Cohen Special Instructions D Only approved calculators are allowed. ts Justily a]l your answers. > All questions have equal va.lue. l Using the Causs Jordan method, flnd all solutions of the following system of equations: 6xz-x3*rl:6 2x2+2r3i3ra:3 8cz 3c: 2ta : 3 rri\ \r.i /r -r r\ ll :l) /1 ro l ln , r l l: 22il \o o 6 2 h.+ 4tt 2 Let M: and 1et B : Calculate ,LI I. Find the matrix C such that MC : B. J ( ) U . ctrm' . -'r,e ,5o " rlc lo11 ting 1' "'1' (r) (b) ,rt,,! 2r+3y i+4a+22 1 '2 -1 \ I I (b) Find the dctenninant of the matrix
MATH 204 Final Examination June 2014 Page 2 of 2 4. (a) FiDd the parametric equations of lhe plane in 1R3 that passes through the point P(1,2,3) and is parallel to both ur: (2,1, 1) andrr:(1,4, 5). (b) Fnrd ihe equation of the plane that contains ihe point