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GATE 2018 ME (ME2) – Question 29

Engineering Mathematics · Linear Algebra: Matrix algebra, systems of linear equations, eigen values and eigen vectors · 1 mark · Numerical answer

For $$A=\begin{bmatrix}1&2&3\\0&4&5\\0&0&1\end{bmatrix},$$ find $\det(A^{-1})$ to two decimal places.

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Correct answer: 0.25 to 0.25

Explanation

A triangular matrix has determinant equal to its diagonal product: $\det A=1(4)(1)=4$. Since $\det(A^{-1})=1/\det A$, the answer is **0.25**.