Question

Find the matrix A

https://i.imgur.com/GH3K93s.png

How do I solve this?

Answer 1

\(\large (A^{-1})^T = (A^T)^{-1}\)

Answer 2

may be work it out by undoing the operations - start by taking the transpose both sides

Answer 3

\[


\left(5A\right)^T =
\left[ \begin{array}{cc}
2&-3 \\
-1&4 \\

\end{array} \right]^{-1}

\]

Answer 4

\[


5A =
\left[ \begin{array}{cc}
2&-1 \\
-3&4 \\

\end{array} \right]^{-1}

\]

Answer 5

How do I deal with the inverse in this problem?

Answer 6

the answer is,

https://i.imgur.com/Uvkdxz3.png

Answer 7

so I assume I cant just divide both sides by 1/5

Answer 8

why not...
5A = t means A = t/5 right

Answer 9

I mean to get the answer

Answer 10

Can I just take the inverse of the inverse on the right to get the answer?

Answer 11

\[A = \dfrac{1}{5}
\left[ \begin{array}{cc}
2&-1 \\
-3&4 \\

\end{array} \right]^{-1}\]

Answer 12

yes just take the inverse

Answer 13

Ok thats what I suspected, I make so many arithmetic errors its probably why I didnt get the correct answer in the first place

Answer 14

http://prntscr.com/3ugsba

Answer 15

thanks, I used the Identity algorithm for some reason

Answer 16

np :) btw whats an identity algorithm ?

Answer 17

Its just when you set up the augmented matrix,

[A | I ] -> row operations -> [ I | A^-1 ]

Answer 18

aahh row operations got you :)