Question

How do i find the inverse of [-1 3]
-4 2

Answer 1

What methods have you learned for finding the inverse of a 2x2 matrix? There is a formula for this purpose. But you could also find the inverse using the Gauss-Jordan Method (which involves row operations). Which method is your teacher using?

Answer 2

So i learned that you multiply the -1 and 4 and subtract the answer from that when you multiply 3 and -4. After that i thought would become that denominator so like 1(1/10) but that must be way off because my answer was wrong.

Answer 3

That method is the "formula method" and applies only to 2 x 2 matrices. Your given matrix is a 2 x 2 matrix.

What are the values of a, b, c and d?

Answer 4

a=-1 b=3 c=-4 d=2 and then i would do ad-bc would be the start right?

Answer 5

yes. show all work, please.

Answer 6

that was what i did and got 1/10 and multiplied it by all the a b c and d values and my answer was wrong.

Answer 7

Be patient, please. How did you get 1/10? I need to see your calculations.

Answer 8

so -1(2)-3(-4)=10 then it becomes 1/10 and multiply it be the a,b,c,d

Answer 9

\[\left| A \right|=\left|\begin{matrix}-1 & 3 \\ -4 & 2\end{matrix}\right|=(-1)2-(-4)3=-2+12=10\]
co-factors of first row are 2,-(-4) i.e.,2,4
co-factors of second row are -(3),+(-1) i.e.,-3,-1
\[adjoint~ A =\left[\begin{matrix}2 & 4 \\ -3 & -1\end{matrix}\right]'=\left[\begin{matrix}2 & -3 \\ 4 & -1\end{matrix}\right]\]
\[A ^{-1}=\frac{ 1 }{ 10 }\left[\begin{matrix}2 & -3 \\ 4 & -1\end{matrix}\right]\]

Answer 10

i got it thank you