MHT CET · Maths · Matrices
The element in the third row and second column of the inverse of the \(\operatorname{matrix}\left[\begin{array}{ccc}3 & 2 & 6 \\ 1 & 1 & 2 \\ 2 & 2 & 5\end{array}\right]\) is
- A \(1\)
- B \(-2\)
- C \(2\)
- D \(0\)
Answer & Solution
Correct Answer
(B) \(-2\)
Step-by-step Solution
Detailed explanation
The element of third row and second column of inverse of a matrix
\(
=\frac{\text { Cofactor of second row and third column of the matrix }}{\text { Determinant of the matrix }}
\)
\(=\frac{-(3 \times 2-2 \times 2)}{3(1 \times 5-2 \times 2)+2(2 \times 2-1 \times 5)+6(1 \times 2-2 \times 1)}\)
\(=\frac{-2}{3-2+0}\)
\(=-2\)
\(
=\frac{\text { Cofactor of second row and third column of the matrix }}{\text { Determinant of the matrix }}
\)
\(=\frac{-(3 \times 2-2 \times 2)}{3(1 \times 5-2 \times 2)+2(2 \times 2-1 \times 5)+6(1 \times 2-2 \times 1)}\)
\(=\frac{-2}{3-2+0}\)
\(=-2\)
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