Question

Which matrix equation can be used to solve the system?

Option 1: [6, 7; 17, 8] * [x; y] = [14; 27]
Option 2: [6x, 7y; 17x, 8y] = [14, 27]
Option 3: [6; 17] * [x, y] = [14; 27]
Option 4: [6x + 7y = 14; 17x + 8y = 27]

Answer 1

The correct matrix equation to solve the system of linear equations is Option 1: [6, 7; 17, 8] * [x; y] = [14; 27], representing a matrix operation that aligns with the coefficients of the variables in the given system, and allows for solving through matrix methods.

Step-by-step explanation:

The correct matrix equation to solve the given system of linear equations is Option 1: [6, 7; 17, 8] * [x; y] = [14; 27]. This option represents a matrix multiplication where the first matrix contains the coefficients of the variables 'x' and 'y' from the original system, and the second matrix represents the column vector of the variables 'x' and 'y'. When multiplied, this matrix equation results in the same set of equations as the original system, which can then be solved using methods such as matrix inversion or row reduction.

In Option 2, the notation is incorrect for matrix representation since it involves specific values for x and y, which are unknown. Option 3 has vector dimensions that do not match for a valid matrix multiplication. Option 4 simply restates the system of equations without using matrix representation.