Question

Find B^-1

Matrice:
[-3 -1]
[-4 -2]

Answer 1

Which method do you have to use to find the inverse?

Answer 2

Nothing specifically. @Hero

Answer 3

Are you aware of the methods that currently exist to find the inverse of a matrix?

Answer 4

I'm just checking this for a friend, I'm not sure how to do this anymore lol.

Answer 5

The two most commonly used computational methods are:

1. Augmented Matrix method
2. Adjoint method

As detailed in this link:
http://www.mathwords.com/i/inverse_of_a_matrix.htm

Answer 6

Can you show me how to do that?

Answer 7

Basically
\[B^{-1} = \frac{1}{\det(B)}\begin{bmatrix} d & -b \\ -c & a \end{bmatrix}\]

Answer 8

So first find the determinant of B which is \(ad - bc\) or rather \((-3)(-2) -(-4)(-1)\)

Answer 9

so \(\det(B) = 6 - 4 = 2\)

Answer 10

So detB is = 2?

Answer 11

Yes, correct. Now, swap \(a\) and \(d\) and then make \(c\) and \(b\) positive to get:

Answer 12

Okay so 1/2 [-2 1]
[4 -2]

Answer 13

\[B^{-1} = \frac{1}{2}\begin{bmatrix} -2 & 1 \\ 4 & -3 \end{bmatrix}\]

Answer 14

Oh whoops missed the -3. Now do I muliply each or what?

Answer 15

Now you do this:
\[B^{-1} = \begin{bmatrix} -2/2 & 1/2 \\ 4/2 & -3/2 \end{bmatrix}\]

Answer 16

Basically divide each value inside the matrix by half

Answer 17

Which afterwards you should end up with:
\\[B^{-1} = \begin{bmatrix} -1 & \frac{1}{2} \\ 2 & -\frac{3}{2} \end{bmatrix}\]

Answer 18

Awesome that's what I got, thanks so much!