Answer:
The answer is (b)
Step-by-step explanation:
* Lets check how to find the inverse of the matrix,
its dimensions is 2 × 2
* To know if the inverse of the matrix exist find the determinant
- If its not equal 0, then it exist
* How to find the determinant
- It is the difference between the multiplication of
the diagonals of the matrix
Ex: If the matrix is [tex]\left[\begin{array}{ccc}a&b\\c&d\end{array}\right][/tex]
its determinant = ad - bc
- After that lets swap the positions of a and d, put negatives
in front of b and c, and divide everything by the determinant
- The inverse will be [tex]\left[\begin{array}{ccc}\frac{d}{ad-bc} &\frac{-b}{ad-bc}\\\frac{-c}{ad-bc} &\frac{a}{ad-bc}\end{array}\right][/tex]
* Lets do that with our problem
∵ The determinant = (9 × 9) - (-2 × -10) = 81 - 20 = 61
- The determinant ≠ 0, then the inverse is exist
∴ The inverse is [tex]\frac{1}{61}\left[\begin{array}{ccc}9&2\\10&9\end{array}\right][/tex]=
[tex]\left[\begin{array}{ccc}\frac{9}{61}&\frac{2}{61}\\\frac{10}{61} &\frac{9}{61}\end{array}\right][/tex]
* The answer is (b)
