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  • State True or False for the statements If the value of a third order determinant is 12, then the value of the determinant formed by replacing each element by its co-factor will be 144.

State True or False for the statements

If the value of a third order determinant is 12, then the value of the determinant formed by replacing each element by its co-factor will be 144.

Answers (1)

\\ \vspace{\baselineskip} Given: $ \therefore $ $ \vert $ A$ \vert $ = 12\\ \vspace{\baselineskip}
For any square matrix of order n, adj A$ \vert $ = $ \vert $ A$ \vert $ \textsuperscript{n-1}\\ \\


\\ \vspace{\baselineskip}For n = 3, $ \vert $ adj A$ \vert $ = $ \vert $ A$ \vert $ \textsuperscript{3-1}\\ \\ \vspace{\baselineskip}= $ \vert $ A$ \vert $ \textsuperscript{2}\\ \\ \vspace{\baselineskip}= 12\textsuperscript{2} = 144\\ \vspace{\baselineskip}

Thus the given statement is true.

Posted by

infoexpert22

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