Prove that vectors (2,1,4), (1,-1,2),(3,1,-2) form a basis of V³(R)
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Step-by-step explanation:
Given:
(2, 1, 4), (1, –1, 2) and (3, 1, –2)
To find:Prove that these vectors for a basis of V³(R).
Solution:
To prove given vectors are the basis for V³(R),we have to prove that all three vectors are linearly independent.
If determinant of all three is not equal to zero,then one can say that all these vectors are independent.
Let
Put these values in determinant
Expand the determinant along R1
=2(2-2)-1(-2-6)+4(1+3)
=0-1(-8)+4(4)
=8+16
=24≠0
Therefore,
Vectors are linearly independent thus form a basis of V³(R)
Thus,
It has been prove that vectors (2,1,4), (1,-1,2),(3,1,-2) form a basis of V³(R).
Hope it helps you.
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