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Unformatted text preview: a = [1,1] and b = [1,1]. (a) (3 marks) Write [5,1] as a linear combination of a and b , that is ﬁnd constants c 1 and c 2 such that [5 , 1] = c 1 a + c 2 b (b) (2 marks) Can any vector x with two components be expressed as a linear combination of a and b ? Justify brieﬂy. 4. Let a = [2, 2, 2] and b = [3, 0, 1]. Find all vectors c such that the vectors a , b , c are linearly dependent (that is they all lie on the same plane). 5. Consider the two lines below, given in paramtetric form L 1 : x = (0 , 1 , 2) + s (1 , , 2) L 2 : x = (4 , 2 , c ) + t (2 , , d ) where c and d are constants. (a) (1 mark) For what value of d are the lines parallel (in the same direction)? (b) (1 mark) With the value of d above, for what value(s) of c (if any) are the two lines identical? Justify brieﬂy. (c) (3 marks) For the case c = 5 and d = 0 ﬁnd the point P on L 1 and Q on L 2 such that the distance between P and Q is as small as possible....
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 Spring '08
 Caddmen
 Math, Linear Algebra, Vectors, Vector Space, Justify briefly

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