Question

Which matrix equation is equivalent to the following matrix equation?

Answer 1

\[\left[\begin{matrix}-1 & -1 \\ 1 & 4\end{matrix}\right]\left(\begin{matrix}x \\ y\end{matrix}\right)=\left(\begin{matrix}-4 \\ 1\end{matrix}\right)\]
A.\[\left(\begin{matrix}x \\ y\end{matrix}\right)=\left[\begin{matrix}-4/3 & -1/3 \\ 1/3 & 1/3\end{matrix}\right]\left(\begin{matrix}-4 \\ 1\end{matrix}\right)\]B.\[\left(\begin{matrix}x \\ y\end{matrix}\right)=\left[\begin{matrix}-1 & 1 \\ 1 & 4\end{matrix}\right]\left(\begin{matrix}-4 \\ 1\end{matrix}\right)\]C.\[\left(\begin{matrix}x \\ y\end{matrix}\right)=\left[\begin{matrix}-1/3 & 1/3 \\ 1/3 & 4/3\end{matrix}\right]\left(\begin{matrix}-4 \\ 1\end{matrix}\right)\]D.\[\left(\begin{matrix}x \\ y\end{matrix}\right)=\left[\begin{matrix}4 & -1 \\ -1 & -1\end{matrix}\right]\left(\begin{matrix}-4 \\ 1\end{matrix}\right)\]

Answer 2

U just got to find the inverse of the matrix given on LHS

Answer 3

I'm not quite sure how to do that.. I know I learned it at some point but I just feel overwhelmed by it right now ._.

Answer 4

I feel like I want to say D, but that's probably wrong...

Answer 5

Let\[A = \left[\begin{matrix}-1 & -1 \\ 1 & 4\end{matrix}\right]\] So \[A ^{-1} = \frac{ adj(A) }{ \left| A \right| }\]

Answer 6

I'm confused by the equation for A^-1 ._. I know it's to get the inverse of A but I'm not sure what adj means or how to get the absolute value of a matrix.

Answer 7

absolute value means to get the determinant of A

Answer 8

Does this help you at all?

Answer 9

Oh! It makes a little bit more sense now. Hold on a second let me see if I can figure this out

Answer 10

Go for it

Answer 11

the determinant of A would be -3? Is that right?

Answer 12

so the inverse of the determinant would be -1/3?

Answer 13

Ya correct go on!!!

Answer 14

so then the equation would be\[-1/3\left[\begin{matrix}4 & 1 \\ -1 & -1\end{matrix}\right]\]
and do I multiply them now?

Answer 15

Ur adj(A) is not correct

Answer 16

Oh, okey dokey, where did I go wrong?

Answer 17

Swap that 1 with the -1 diagonally (coz u have to take apply transpose property too)

Answer 18

so then it would be?\[-1/3\left[\begin{matrix}4 & -1 \\ 1 & -1\end{matrix}\right]\]

Answer 19

Yup and now just multiply

Answer 20

so it would be?\[\left[\begin{matrix}-4/3 & 1/3 \\ -1/3 & 1/3\end{matrix}\right]\]

Answer 21

Yes but its not in the options

Answer 22

hm, that's weird lol. i'll just pick the one it's closest to then and hope for the best.

Answer 23

thank you so much!

Answer 24

yw.
Btw I think that the our answer is right and the options are wrong... Let me check once again

Answer 25

It's not -1/3 It's
\[\frac{ 1 }{ 3 }\left[\begin{matrix}4 & -1 \\ 1 & -1\end{matrix}\right]\] Giving you
\[\left[\begin{matrix}4/3 & -1/3 \\ 1/3 & -1/3\end{matrix}\right]\]
Which still isn't one of the choices.