Prove that the vectors (2, 1, 4), (1, –1, 2) and (3, 1, –2) for 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
Determinant ≠ 0
Therefore,one can conclude that,
Vectors are linear independent thus form a basis for V³(R).
Hope it helps you.
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1) Two matrixes A and B are given. Express B^-1 through x and A.
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