Question

Given (C^T -2I)^-1 =|2 1 | find C
|-1 0 |

Answer 1

how do i un-inverse?

Answer 2

what is T here ??

Answer 3

The transpose of the matrix

Answer 4

ohhh....

Answer 5

the 2I is 2 times the unit matrix and the ^-1 is the inverse of the entire matrix

Answer 6

u know how we find inverse of matrix of order 2X2

Answer 7

take inverse on both side

Answer 8

find inverse
\[(A^{-1})^{-1} = A\]

Answer 9

\[(A^{-1})^{-1}=A\]

Answer 10

1/|C| | b -d |
|-c a |

Answer 11

so the inverse on the left is |0 1|
|-1 2|

Answer 12

and then i just add 2I on the right and transpose it?

Answer 13

we also multiply by -1

Answer 14

and divide by determinent

Answer 15

its 1/1 since |C|=2(0)-1(-1)=1

Answer 16

\[\left[\begin{matrix}0 & -1 \\ 1 & 2\end{matrix}\right]\]

Answer 17

\[C^T-2I\]

Answer 18

above matrix equal to this

Answer 19

\[2I=\left[\begin{matrix}2 & 0 \\ 0 & 2\end{matrix}\right]\]

Answer 20

but if i use the formula |a b|=|b -c|
|c d| |-d a|

Answer 21

but u forgot to multiply by -1

Answer 22

then the -1 in c will swap with the 1 in b and then multiply both by -1

Answer 23

i see i confused myself with the signs

Answer 24

we dont swap b and c

Answer 25

youre right

Answer 26

only a and d are swapped

Answer 27

i see, my formula was wrong

Answer 28

now after that add 2I on both side in \[C^T-2I\]

Answer 29

and matrix on left side

Answer 30

thanks

Answer 31

welcome :)