Question

Inverse Matrices and Systems help. @mathmale

Will put picture up..

Answer 1

What is the solution of the matrix equation? Can you please explain to me how to do this?

Answer 2

\(
\left[ {\begin{array}{cc}
9 & 4 \\
2 & 1 \\
\end{array} } \right]
\large X=\)\(
\left[ {\begin{array}{cc}
-9 & -6 \\
-1 & -8 \\
\end{array} } \right]
\)
\[\det(
\left[ {\begin{array}{cc}
9 & 4 \\
2 & 1 \\
\end{array} } \right]
)=9-8\ne1\] so \(
\left[ {\begin{array}{cc}
9 & 4 \\
2 & 1 \\
\end{array} } \right]
\) is invertable, so \(\large X=
\left[ {\begin{array}{cc}
9 & 4 \\
2 & 1 \\
\end{array} } \right]^{-1}
\)\(
\left[ {\begin{array}{cc}
-9 & -6 \\
-1 & -8 \\
\end{array} } \right]
\)

For a \(2\times 2\) matrix \(A=
\left[ {\begin{array}{cc}
a & b \\
c & d \\
\end{array} } \right]
\) we have \(A^{-1}= \frac{1}{ad-bc}
\left[ {\begin{array}{cc}
d & -b \\
-c & a \\
\end{array} } \right]
\)
so you have \(\large X = \frac{1}{1}
\left[ {\begin{array}{cc}
1 & -4 \\
-2 & 9 \\
\end{array} } \right]

\left[ {\begin{array}{cc}
- 9 & -6 \\
-1 & -8 \\
\end{array} } \right]
\)

Answer 3

What? I don't understand..

Answer 4

@mathmale

Answer 5

what part do you not understand?

Answer 6

The whole thing.. I don't know what "det" means either.

Answer 7

do you know what the determinate of a matrix is?

Answer 8

Not really, I have had some trouble with these last sections of matrices in my book..

Answer 9

do you know how to tell if a 2by 2 matrix is invertable?

Answer 10

If it times to 1?

Answer 11

I will be right back, I have to eat dinner.. If you could please write out the problem in a different way, maybe that would help..

Answer 12

Okay, I'm back. Could you help?