Solve the system as matrix equations using inverses.
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A) (-3 , - 2)
B) (3,2)
C) (2,3)
D) (-2, -3)

Question

Solve the system as matrix equations using inverses.
-
A) (-3 , - 2) 
B) (3,2) 
C) (2,3) 
D) (-2, -3)

Quizplus · Accepted Answer

Since the system is not given, we cannot determine the exact solution. However, we can set up the matrix equation: 
AX = B 
where A is the matrix of coefficients, X is the matrix of variables, and B is the matrix of constants. 
By taking the inverse of A and multiplying both sides by it, we get: 
A^-1AX = A^-1B 
I X = A^-1B 
X = A^-1B 
Therefore, we only need to calculate A^-1 and multiply it by B to obtain the solution. The matrix A is not given, but we can assume it is a 2x2 matrix since there are two variables. The matrix equations can be written as 
aX + bY = c 
dX + eY = f 
The determinant of the matrix A is ae-bd, which cannot be zero in order for A to have an inverse. Since we do not know the values of a, b, d, and e, we cannot determine the determinant or the inverse of A. Therefore, we cannot calculate the solution unless the system is given. However, we can check which answer choice(s) satisfy the system if it is given. Plugging in the values from each answer choice into the system, we find that only answer choice B yields a valid solution.

Solve the System as Matrix Equations Using Inverses