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Determinants and Matrices — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsDeterminants and Matrices1 Mark
Question
Evaluate:

$\left|\begin{array}{ccc}1 & -3 & 12 \\ 0 & 2 & -4 \\ 9 & 7 & 2\end{array}\right|$

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Answer

$\left|\begin{array}{ccc}1 & -3 & 12 \\ 0 & 2 & -4 \\ 9 & 7 & 2\end{array}\right|$

$=1\left|\begin{array}{rr}2 & -4 \\ 7 & 2\end{array}\right|-(-3)\left|\begin{array}{rr}0 & -4 \\ 9 & 2\end{array}\right|+12\left|\begin{array}{ll}0 & 2 \\ 9 & 7\end{array}\right|$

= 1(4 + 28) + 3(0 + 36) + 12(0 – 18) = 1(32) + 3(36) + 12(-18) = 32 + 108 – 216 = -76

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