Question

Which matrix equation can be used to solve the system?
(2x+ 5y = 15
X + 3y = 18

Answer 1

option 3

Explanation:

`AX = B\\X = A^(-1)B\\\\A = \left[\begin{array}{CC}\\2&5\\1&3\end{array}\right]\\\\\\B =\left[\begin{array}{C}\\15&18\end{array}\right]\\\\\\X =\left[\begin{array}{C}\\x&y\end{array}\right]`

`det A = 1\\\\adj A = \left[\begin{array}{CC}\\3&-5\\-1&2\end{array}\right]`

`A^(-1) = (1)/(det A) * Adj A`

`= 1 * \left[\begin{array}{CC}\\3&-5\\-1&2\end{array}\right]\\\\\\= \left[\begin{array}{CC}\\3&-5\\-1&2\end{array}\right]`

Therefore,

`X = A^(-1)B\\\\\\\left[\begin{array}{C}\\x&y\end{array}\right] = \left[\begin{array}{CC}\\3&-5\\-1&2\end{array}\right]\left[\begin{array}{C}\\15&18\end{array}\right]\\\\\\`

Answer 2

THE CORRECT OPTION IS A where the input data is correct