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MTH501 Assignment 01 Spring 2021 Solution / Discussion

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MTH501 Assignment 01 Spring 2021 Solution

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MTH 501

Assignment No. 1

Question No. 1

as indexed set of vectors {v, v .......v } in R n is said to be linearly independent in the vector

1   2         n

equation x1v1 +x2v2+x3v3               xnvn=0 has only the trivial solution

First, we write the argument matrix of the given vectors

 

Row operation on the associated augmented matrix show that

        

 

 

 

This is clear that there are three basic variables and no free variable so the given set if vectors is linearly independent.

b)

First, we write the argument matrix of the given vectors

 

Row operation on the associated augmented matrix show that

 

 

Clearly x1 and x 2 are basics variables and x3 is the free variable So that the given set of vectors is not linearly independent.

 

Question No. 2

First, we write the argument matrix of the given vectors

 

Row operation on the associated augmented matrix show that

 

 

 

 

So, the solution is unique when

 

 

 

 

 

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