Exams Joint Entrance Examination Mathematics Matrices and Determinants Question 353 Question 353 of 472 Medium MCQ
If \[B = \left[ { ( 5 2 α 1 0 2 1 α 3 − 1 ) \begin{pmatrix} 5 & {2\alpha } & 1 \\
0 & 2 & 1 \\
\alpha & 3 & { - 1} \\ \end{pmatrix} 5 0 α 2 α 2 3 1 1 − 1 } \right]\] is the inverse of a 3 \times 3 matrix A, then the sum of all values of \[\alpha \] for which
det(A) + 1 = 0, is :
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Given |A| + 1 = 0
\[ \Rightarrow \] |A| = -1
\[\left| B \right| = \left| {{A^{ - 1}}} \right| = {1 \over {\left| A \right|}} = - 1\]
\[\left| { ( 5 2 α 1 0 2 1 α 3 − 1 ) \begin{pmatrix} 5 & {2\alpha } & 1 \\
0 & 2 & 1 \\
\alpha & 3 & { - 1} \\
\end{pmatrix} 5 0 α 2 α 2 3 1 1 − 1 } \right| \] = -1
\[ \Rightarrow \] \[ 5( - 2 - 3) + 2\alpha (\alpha ) + 1( - 2\alpha ) = - 1\]
\[ \Rightarrow \] \[2{\alpha ^2} - 2\alpha - 24 = 0\]
\[ \therefore \] sum of value of \[\alpha \] = \[{{ - ( - 2)} \over 2} = 1\] Answer the question to unlock