Find the det(-2A) and compare it to det(A) for A={1 1}{3 -1}
Solution:-
solving det(A)
we get
∣113−1∣=(1)⋅(−1)−(1)⋅(3)=−4\left|\begin{array}{cc}1 & 1\\3 & -1\end{array}\right| = \left(1\right)\cdot \left(-1\right) - \left(1\right)\cdot \left(3\right) = -4∣∣131−1∣∣=(1)⋅(−1)−(1)⋅(3)=−4 ................(1)
we know the property of determinant
det(xA)=det(xA)=det(xA)= xndet(A)x^ndet(A)xndet(A) where n is the order .
here
det(−2A)=det(-2A)=det(−2A)= (−2)2det(A)(-2)^2det(A)(−2)2det(A)
=4(−4)=4(-4)=4(−4) ...............(from 1)
=−16=-16=−16
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