Question

Help with matrices?
http://gyazo.com/01dab9703051b6c97cee4b2038ab1dbe

Answer 1

The matrix will have an inverse if the determinant is nonzero.

Answer 2

so the determinant is -99

Answer 3

No, recheck your arithmetic. But you're right in that the determinant is still nonzero.
\[\begin{vmatrix}-7&-25\\2&7\end{vmatrix}=-7\times7-2\times(-25)=-49+50=1\]

Answer 4

i did (-49)+(-50)

Answer 5

But for a 2x2 matrix \(\begin{bmatrix}a&b\\c&d\end{bmatrix}\), the determinant is
\[\begin{vmatrix}a&b\\c&d\end{vmatrix}=ad-bc\]
Here, \(a=-7\) and \(d=7\), so \(ad=-49\); \(b=-25\) and \(c=2\), so \(bc=-50\).

So,
\[ad-bc=-49-(-50)=-49+50=1\]

Answer 6

ooh for some reason i thought you were supposed to add

Answer 7

how do you find the inverse since its nonzero

Answer 8

If the determinant of \(\begin{bmatrix}a&b\\c&d\end{bmatrix}\) is nonzero, as it is in this case, there's a quick formula you can use for 2x2 matrices. The inverse of \(\begin{bmatrix}a&b\\c&d\end{bmatrix}\) is
\[\begin{bmatrix}a&b\\c&d\end{bmatrix}^{-1}=\frac{1}{\text{determinant}}\begin{bmatrix}d&-b\\-c&a\end{bmatrix}\]

Answer 9

im not really sure how to work the equation thing so it might take me a second to write what im trying to say

Answer 10

so its 1/1 [7/-2 25/-7]

Answer 11

if you can understand that

Answer 12

Yeah I got it, you mean to write
\[\begin{bmatrix}7&25\\-2&-7\end{bmatrix}\]
which is exactly right.

Answer 13

so thats the answer?

Answer 14

Yes

Answer 15

thank you, that was easier then i expected