Given the matrix C, find a matrix X such that $( X ^T-2I)^{-1}=C$

Question

$$C=\begin{bmatrix}-1 & 1 \\4 & 2 \end{bmatrix}$$

if somebody can help me to solve this question i tried to solve it but no luck while i was trying i thought that if i got C inverse and then add it by I (identity matrix) which makes it transpose = X i do not know if thats right
it will be amazing if someone helped me

thanks

I am glad that you tried. would you like to include what you have tried and we can try to get you unstuck. — Siong Thye Goh, Nov 06 '17 at 04:12

score 1 · Accepted Answer · answered Nov 06 '17 at 04:13

1

$$\quad{( X ^T-2I)^{-1}=C\\ (( X ^T-2I)^{-1})^{-1}=C^{-1}\\( X ^T-2I)=C^{-1}\\X^T-2I=C^{-1}\\X^T=2I+C^{-1}\\X=(2I+C^{-1})^T}$$

answered Nov 06 '17 at 04:13

Khosrotash

24,922

@yara : $C$ is not a square matrix ? – Khosrotash Nov 06 '17 at 04:15
Very nice, I think $C$ is a square matrix – Bensstats Nov 06 '17 at 04:15
the question doesn't make sense then – Bensstats Nov 06 '17 at 04:16
can i ask sth how do you understand how to get the x – yara Nov 06 '17 at 04:22
i always get stuck when they ask me to find x – yara Nov 06 '17 at 04:22
$C_{2\times 2}$ matrix ,so $I_{{2\times 2}}$ matrix too . then $X^T ,X$ must be 2*2 . – Khosrotash Nov 06 '17 at 04:24
1

oh got it thanks alt – yara Nov 06 '17 at 04:25

Given the matrix C, find a matrix X such that $( X ^T-2I)^{-1}=C$

1 Answers1