Use an inverse matrix to solve each system of linear equations.
A) x+2y=-1 B)x+2y=10 C)x+2y=-3
x-2y=3 x-2y=-6 x-2y=0
To use an inverse matrix to solve a system of linear equations, we need to represent the system in matrix form. Let's write down the augmented matrix for each system of equations.
A) The system of equations is:
x + 2y = -1
x - 2y = 3
The augmented matrix for this system is:
[ 1 2 | -1 ]
[ 1 -2 | 3 ]
B) The system of equations is:
x + 2y = 10
x - 2y = -6
The augmented matrix for this system is:
[ 1 2 | 10 ]
[ 1 -2 | -6 ]
C) The system of equations is:
x + 2y = -3
x - 2y = 0
The augmented matrix for this system is:
[ 1 2 | -3 ]
[ 1 -2 | 0 ]
Now, to solve the systems using an inverse matrix, we need to compute the inverse of the coefficient matrix [A] and then multiply it by the augmented matrix [B]. Let's denote the inverse matrix as [A]⁻¹ and the augmented matrix as [B].
The solution to each system can be obtained as follows:
[A]⁻¹ * [B]
Note that the inverse of a matrix exists only if the determinant of the matrix is non-zero.
Let me now perform the calculations and give you the solutions.