Question

Which matrix represents the solution to the given system of equations?

A) 1 0
-2 0
B) 1 0
1 0
C) -2 1
0 0
D) 0 1
0 0

Answer 1

The matrix that represents the solution to the given system of equations is Option C) -2 1 0 1 0 0. To solve the system of equations, we need to write it in matrix form (AX = B), where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix. The coefficient matrix is given by A = 1 0 -2 1. The constant matrix is B = 0 1. To find the solution X, we can use the formula X = A^(-1)B, where A^(-1) is the inverse of matrix A. In this case, the inverse of A is A^(-1) = -2 0 -2 1. Multiplying A^(-1) and B gives us X = -2(0) + 0(1) = 0 -2(0) + 1(1) = 1, which is the solution to the system of equations.

Step-by-step explanation:

The matrix that represents the solution to the given system of equations is Option C) -2 1
0 1
0 0.

To solve the system of equations, we need to write it in matrix form (AX = B), where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix. The coefficient matrix is given by A = 1 0
-2 1. The constant matrix is B = 0
1. To find the solution X, we can use the formula X = A^(-1)B, where A^(-1) is the inverse of matrix A.

In this case, the inverse of A is A^(-1) = -2 0
-2 1. Multiplying A^(-1) and B gives us X = -2(0) + 0(1) = 0
-2(0) + 1(1) = 1, which is the solution to the system of equations.