MTH501 Assignment 01 Spring 2021 Solution / Discussion
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MTH501 Assignment no 1 Solution Spring 202
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MTH501 Assignment 1 Solution Spring 2021 | MTH501 Assignment 1 Solution 2021
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 x_{1}v_{1} +x_{2}v_{2}+x_{3}v_{3 } x_{n}v_{n}=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 x_{1} and x _{2} are basics variables and x_{3} 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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