Question #206957

Find the det(-2A) and compare it to det(A) for A={1 1}{3 -1}


1
Expert's answer
2021-06-15T09:16:15-0400

Solution:-

solving det(A)

we get

1131=(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 ................(1)

we know the property of determinant

det(xA)=det(xA)= xndet(A)x^ndet(A) where n is the order .

here

det(2A)=det(-2A)= (2)2det(A)(-2)^2det(A)

=4(4)=4(-4) ...............(from 1)

=16=-16


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