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GATE Overflow | Mathematics | Test 1 | Question: 23
Bikram
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Linear Algebra
Aug 8, 2016
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If the determinant of an $n \times n$ matrix $A$ is zero then
rank of $A$ is $n$
rank of $A\leq n-2$
$A$ has at least one zero eigen value
the system of equations $Ax=0$ has no solution other than trivial solution
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Bikram
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Best answer
Product of Eigen values = Determinant
Determinant is 0 i.e. one of the Eigen Value is 0
Digvijay Pandey
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Sep 13, 2016
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Sep 13, 2016
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Arjun
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for a singular matrix product of eigen value is zero
product of eigen value is equal det of matrix and sum is equal to trace
abhishek tiwary
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Jul 7, 2017
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abhishek tiwary
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Answer:
C
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