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TIFR-2011-Maths-B-1

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makhdoom ghaya asked Dec 10, 2015
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Any non-singular $k \times k$-matrix with real entries can be made singular by changing exactly one entry.
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If $A$ and $B$ are $3 \times 3$ matrices and $A$ is invertible, then there exists an integer $n$ such that $A + nB$ is invertible.
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makhdoom ghaya asked Dec 9, 2015
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Let $A$ be a $5 \times 5$ matrix with real entries, then $A$ has An eigenvalue which is purely imaginary At least one real eigenvalue At least two eigenvalues which are not real At least $2$ distinct real eigenvalues
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makhdoom ghaya asked Dec 9, 2015
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$A$ is $3 \times 4$-matrix of rank $3$. Then the system of equations, $Ax = b$ has exactly one solution.
$A$ is $3 \times 4$-matrix of rank $3$. Then the system of equations,$Ax = b$has exactly one solution.
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