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Question

Mathematics Question on Determinants

Write the cofactors of each element of the first column of the following matrices. A=[4−12 1−32 352]A=\left[\begin{matrix}4&-1&2\\\ 1&-3&2\\\ 3&5&2\end{matrix}\right]

A

4,−12,−164, -12 , -16

B

4,12,164, 12, 16

C

−4,−12,−16-4, -12 , -16

D

−16,12,4-16, 12, 4

Answer

−16,12,4-16, 12, 4

Explanation

Solution

M11=∣−32 52∣=6−10=−6⇒c11=M11=−16M_{11}=\left|\begin{matrix}-3&2\\\ 5&2\end{matrix}\right|=6-10=-6 \Rightarrow c_{11}=M_{11}=-16 M21=∣−12 52∣=−2−10=−12⇒c21=−M21=12M_{21}=\left|\begin{matrix}-1&2\\\ 5&2\end{matrix}\right|=-2-10=-12 \Rightarrow c_{21}=-M_{21}=12 M31=∣−12 −32∣=−2+6=4⇒c31=M31=4M_{31}=\left|\begin{matrix}-1&2\\\ -3&2\end{matrix}\right|=-2+6=4 \Rightarrow c_{31}=M_{31}=4