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Unformatted text preview: Express the vector [2, 1, 0] as a linear combination of a , b and c . 4. (5 marks) Let a = [7, 1, 0] and b = [2, 0, 1]. Find all vectors c such that the vectors a , b and c are linearly dependent (that is they all lie on the same plane). 5. Consider the three planes P 1 , P 2 and P 3 de²ned by: P 1 : x + 2 yz = 5 P 2 : c x + y + z =2 P 3 : d x2 y + h z = 11 where c , d and h are constants. (a) (2 marks) Find all constants c , d and h such that these three planes intersect in a single point. (Do not fnd the intersection point.) (b) (2 marks) For which values o± d and h are the two planes P 1 and P 3 parallel? ( Hint : use the vectors normal to these planes.) (c) (1 mark) For what value o± c are the two planes P 1 and P 2 parallel?...
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 Spring '08
 Caddmen
 Math, Linear Algebra, Vectors, Vector Space

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