Answer to Question #206957 in Linear Algebra for Blackvey

Question

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

Answer 1

Solution:-

solving det(A)

we get

$\left|\begin{array}{cc}1 & 1\\3 & -1\end{array}\right| = \left(1\right)\cdot \left(-1\right) - \left(1\right)\cdot \left(3\right) = -4$ ................(1)

we know the property of determinant

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

here

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

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

$=-16$