LINEAR ALGEBRA TEST #2 SOLUTIONS |
Note: all vectors are diplayed vertically.
1)
a) det(A) = -1 |
b) adj(A) = |
c) A-1 = |
d) |
(10)
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2) u = , v = , w = .
a) | b) | c) É u + v É = |
d) cos h = 0 so h = 90° | e) Area = || v % w || = | |
f) proj V u = |
(15)
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3) a) w = .
b) x = u % v = .
c) y = .
d) u $ v = 1 ! 0 so vectors are not orthogonal.
e) 3u $ (u - 2v) = 9
(10)
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4) a)
b) Find vectors PQ and PR then cross product to find the normal =
so the equation of the plane is -4x - 8y + 4z + 4 = 0 or x + 2y - z - 1 = 0
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c)
d) The point of intersection is (44/13, 19/13, 40/13) since t = 6/13 .
e) When t = 1 and s = -1 the lines intersect at (2, -1, 6)
f) normal of plane = dotted with the line's direction vector = 0. So l // plane.
(15)
TOTAL (50)
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