How to find the determinant of the matrix here ?

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Answer 1 · 2018-04-15T17:44:14

(A) and (D)

$adj(P)$ $=$ $((1,4,4),(2,1,7),(1,1,3))$

Edit:
$|(color(red)1, color(blue)4, color(green)4), (color(green)2 ,color(red)1, color(blue)7), (color(blue)1, color(green)1, color(red)3)|$

We multiply the same colors and add them and then we subtract when we multiply the same colors but from this scheme:

$|(color(brown)1, color(orange)4, 4),(color(orange)2, 1, color(brown)7), (1, color(brown)1, color(orange)3)|$

So we have:
$color(red)3+color(blue)28+color(green)8-4-color(orange)24-color(brown)7=4$

Now, since this is the adjoint matrix, and the matrix is 3x3, there is a formula:

$det(adj(A))=(det(A))^(n−1)$

where n is the number of rows in the matrix.

So, we will have
$4=det(A)^2$
$sqrt4=sqrt(det(A)^2)$
$2=|det(A)|$ .........................{NOTE that $sqrt(x^2)=|x|$ }
$:. det(A) = +-2$

So the answer is A and D.

I hope this helped you.