Question

The matrix below represents a system of equations. What describes the solution to this system of equations?

1) No solution
2) Unique solution
3) Infinite solutions

Answer 1

The given matrix represents an identity matrix, indicating a unique solution to the system of equations. Therefore, the correct option is 2).

Step-by-step explanation:

The matrix [1 0 0] [0 1 0] [0 0 1] represents an identity matrix. In a system of equations, an identity matrix means that each variable has a coefficient of 1 in a single equation and 0 coefficients in all other equations. This means that the system has a unique solution, as each variable can be solved independently without any dependencies on each other.

In this case, each row in the matrix corresponds to an equation with one of the variables equal to one, and the rest zero. Thus, the system of equations here would be x = 1, y = 1, and z = 1, which are explicit solutions without any need for further calculation or conditions.

Therefore, the matrix represents the identity matrix, corresponding to a system of equations with a unique solution for each variable. Therefore, the correct option is 2).