Question

How do I invert this matrix (or show that it is singular)?

(1 4
-2 3)

Answer 1

If you mean inverse by invert then:
if the Determinant=0 then it doesn't have an inverse
So let: \[A=\left[\begin{matrix}a & b \\ c & d\end{matrix}\right] \quad \text{then} \quad A^-1=\frac{ 1 }{ detA }\left[\begin{matrix}d & -b \\ -c & a\end{matrix}\right]\]

if you don't then sorry! :-)

Answer 2

det(a)=ad-bc

Answer 3

The determinant is 3-(-8) = 11.
So i scalar multiply the matrix
(1 -4
2 3) by 1/11?

Answer 4

yes, you just need to swap the 1 and 3 around (check, a and d swap!)
but yep that's the right idea

Answer 5

Woops, I meant
(3 -4
2 1)
Yes, so I will get a lot of decimals?

Answer 6

just leave it in fraction form if I was you, more accurate technically

Answer 7

Ok... one more thing, what would be the case if the matrix was singular? is that when the determinant is zero?

Answer 8

Exactly!