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Use the inverse of the coefficient matrix to solve the system of equations.

x+2y+3z = 12
2x + 3y + 4z = -9
-x-2y - 4z = -3

User Subha
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Final answer:

To solve the given system of equations using the inverse of the coefficient matrix, you need to convert the system into matrix form AX = B, compute the inverse of the coefficient matrix A, and then multiply the inverse with the constants matrix B to get the solution matrix X.

Step-by-step explanation:

To solve the system of equations using the inverse of the coefficient matrix, you will first need to express the system in matrix form as AX = B, where A is the coefficient matrix, X is the column matrix of the variables, and B is the column matrix of constants. For the given system:

  • x + 2y + 3z = 12
  • 2x + 3y + 4z = -9
  • -x - 2y - 4z = -3

The matrix form would be:

A = [[1, 2, 3],[2, 3, 4],[-1, -2, -4]],
X = [[x], [y], [z]],
B = [[12], [-9], [-3]]

Next, you will calculate the inverse of matrix A, denoted as A⁻¹, using a mathematical software or a calculator. Once you have A⁻¹, you can find the solution by multiplying it with matrix B to get :

X = A⁻¹B

The resulting matrix X will provide you with the values of x, y, and z that solve the system.

User Rahul Kalidindi
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