111-2001&amp;2002-3-M20-July2002

# 111-2001&amp;2002-3-M20-July2002 - Kuwait University...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

## This note was uploaded on 02/23/2010 for the course LINEAR 0410111 taught by Professor Linear during the Spring '10 term at Kuwait University.

### Page1 / 2

111-2001&amp;2002-3-M20-July2002 - Kuwait University...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online