If a $3 \times 3$ matrix has determinant zero, then is it possible that its rank could be $3$? I think it only could be $2$ or less. I am right or wrong? Please explain.
Rank of a matrix
9
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linear-algebra
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2Yes you are correct. The rank is the number of non-zero singular values and the determinant is the product of these singular values. – 2011-05-18