111-2001&2002-3-M20-July2002

111-2001&2002-3-M20-July2002 - Kuwait University,...

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Unformatted text preview: Kuwait University, Faculty of Science ‘ Dept. of Mathematics 35 Computer Science Second Mid-Term in LINEAR ALGEBRA (Math. 111) Time: 75 min. July 22, 2002 M Calculators, pagers and mobile phones are NOT allowed. Answer the following questions:(Each subquestion is worth 2.5 points) 1. (a) Show that if A is a nonsingular matrix, then (1de is nonsingular and (adeT1 = IJTIA = adj(A'1). 1 —4 3 (b) Let A = 0 ——1 5 . Compute |2adj(A"])l. 0 0 2 2. (a) Show that U + V “2:” U H2 + V M2 if and only if U - V = 0. (b) Find a unit vector perpendicular to both X=C3i_j+3kandY=—22'+j——2k. 3. Let P1132133 be the triangle of vertices P1(1,1,O), P2(0,1,I1) and P3(1, O, 1). (a) Determine whether or not Pl P2133 is a right triangle. (bl Find the area of P1132133. 4. (a) Find an equation of the plane passing through the points 131(0, 1, 2), P2(l, 2, and P3(—l, 2, O). @ Find parametric equations of the line of intersection of the planes x—2ywlOzl-1=Oand3$+y~22+3n0 5. (a) Let W = {(a, b, c, d) e R4 : a+b : c-l— d}. Show that W is a subspace of R4. ® Prove that the vectors V1 2 (1,1,1),V2 = (1,1,0) and V3 = (1,0,0) span R3. GOOD LUCK. OO 99 Jun.) V I, T19d3kk"\'\ = f\c-d3<&>f‘\\ :1 \fi‘ 1+". on ;L\ B) \7/ (“WM-N in IR} @2905) :2 C\£\>\)\\ +C1Lk)\}o)*c “3—5 CI”? C1. «rcg 2‘ng C\-\-C_-2._ :b M) CLZC,C1:\3..C}C.73_ OO 99 ...
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111-2001&amp;amp;2002-3-M20-July2002 - Kuwait University,...

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