I am learning Rank of Matrix chapter, here I am stuck on finding the submatrices for $3\times3$ matrix and also, in case if $3\times2$ matrix is generated as submatrix for $3\times3$ matrix, I wonder how to calculate the determinant value for the following matrix. Since I am new to the topic, any kind of help will be appreciated.
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2$\begingroup$ I don't follow your question talking about $3\times 2$ matrices... only square matrices have determinants. As for how to take a determinant of a $3\times 3$ matrix, there are surely hundreds or thousands of tutorials easily found throughout the internet and on this site as well that should satisfy you. $\endgroup$– JMoravitzCommented Jan 10, 2020 at 14:46
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$\begingroup$ I recommend PatrickJMT's videos on the subject. youtube.com/watch?v=21LWuY8i6Hw $\endgroup$– JMoravitzCommented Jan 10, 2020 at 14:49
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$\begingroup$ The sub-matrices generated in the evaluation of determinant of a given matrix are always square. In the case of $3\times 3$ matrix, there are 3 different sub-matrices and they are all $2\times 2$ matrices. $\endgroup$– YNKCommented Jan 10, 2020 at 16:01
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Determinant is not defined for non-square matrices. Probably, you want to check whether rows of submatrix are linear-independent. To do so there are many different approaches, for example Gaussian elimination.
