GATE ME 2014 Set 1 — Question 15
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Engineering Mathematics → Linear Algebra → Determinants & Inverses
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Question
Which one of the following describes the relationship among the three vectors, , and ?
Correct answer
(B) The vectors are linearly dependent
Solution
Let the three vectors be , , and .
To check for linear dependence, we calculate the determinant of the matrix formed by these vectors:Since the determinant is zero, the vectors are linearly dependent. Alternatively, we can observe that .
To check for linear dependence, we calculate the determinant of the matrix formed by these vectors:Since the determinant is zero, the vectors are linearly dependent. Alternatively, we can observe that .
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