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Vectors

Cool goIITian

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8 Feb 2012 17:03:19 IST

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pls explain the linear combination of vectors

Mathematics

pls explain the linear combination of vectors

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Manasi

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Joined: 1 Dec 2006

Posts: 2108

11 Feb 2012 12:28:12 IST

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If one vector is equal to the sum of scalar multiples of other vectors, it is said to be a linear combination of the other vectors.

For example, suppose a = 2b + 3c, as shown below.

	11
	16

	1
	2

	3
	4

	21 + 33
	22 + 34

Note that 2b is a scalar multiple and 3c is a scalar multiple. Thus, a is a linear combination of b and c.

Vishal Mahuli

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Joined: 14 Feb 2012

Posts: 188

17 Feb 2012 18:15:37 IST

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Manasi has given a perfect answer..... if a vector is equal to the sum of scalar multiples of other 2 vectors then it is clled linear combination.... It is called so becozz... IF A VECTOR IS EUAL TO SUM OF OTHER TWO THEN ALL TH THREE MUST LIE IN A SAME PLANE... SO THEY BECOME COPLANAR and hence called as LINEAR COMBINATION..

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