Final answer:
The matrix equation equivalent to the given system is represented as AX=B, where A is the matrix of coefficients, X is the matrix of variables, and B is the matrix of constants. After calculating the inverse matrix of A, it's multiplied by B to solve for X. The solution to the system is x=1 and y=2.
Step-by-step explanation:
To write a matrix equation that is equivalent to the given system of equations:
2x + 3y = 5
3x + 5y = 8
We can express this system as AX=B, where A is the matrix of coefficients, X is the column matrix of variables, and B is the column matrix of constants:
A = \begin{bmatrix} 2 & 3 \\ 3 & 5 \end{bmatrix}
X = \begin{bmatrix} x \\ y \end{bmatrix}
B = \begin{bmatrix} 5 \\ 8 \end{bmatrix}
To find the solution using the inverse matrix, we need to calculate A-1 and then multiply it by B:
A-1B = X
Following the steps to find the inverse, we get:
A-1 = \begin{bmatrix} 5 & -3 \\ -3 & 2 \end{bmatrix}
Then, we calculate the product of A-1 and B:
X = A-1B = \begin{bmatrix} 5 & -3 \\ -3 & 2 \end{bmatrix} * \begin{bmatrix} 5 \\ 8 \end{bmatrix} = \begin{bmatrix} 1 \\ 2 \end{bmatrix}
Thus, the solution to the system is x = 1 and y = 2.