# 10 Let the planes 1 and 3 be given...

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CONCORDIA UNIVERSITY Department of Mathematics and Statistics Course Number Section(s) , Mathematics 204 All E~Lcepi tC Examination Date Pages Final April 2017 3 Instructors Course Examiner C. L. Santana, F. Mobasheramini, T. Hughes A. Kokotov Special Instructions: Only approved calculators are allowed ! 1. [10] Solve the system of equations z1+2z2—3\$3+x4=1 3x1—x2—x3+2\$4=3 2\$1+6x2+4x3—m4=11 —5x1+m2—x3+7x4=2 2x1—4x2+x3+5x4=4 2. [10] Solve the following equation for (3 x 3) matrix X: 211 111 X—O31X=010 104 101 3. [10] For which a the following matrix a+1 1 1 1 (1+2 (1 2 2 a+2 1 a+2 2 2a+3 1 1 (1+3 is not invertible?
MATH 204 Final Examination April 2017 Page 2 of 3 4. [10] Let the planes (1 and 3 be given by equations (a) :c + y z = 1 and (5) x~y+2z= —1 and let P be the point (2,1,1). (A) Write down the equation of the plane passing through the point P and the line L of intersection of a and B. (B) Find the coordinates of the intersection of the line L and the plane 2x—5y+2=4 5. [10] Find a for which all three vectors (1,2,3), (1, 2+ a, 6) and (1, 10, a— 1) are parallel to the same plane. 6. [10] Find the