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Write the given system of equations as a matrix equation and solve by using inverses.

-2x₁ + x₂=k₁
13x₁-8x₂ -2x₃ = K₂
-X₁ X₃ = K₃

User Arunas
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Final answer:

To solve the given system of equations as a matrix equation and use inverses to find the solution for X, we need to represent the equations as a coefficient matrix, variable matrix, and constant matrix. Then, we can multiply both sides of the equation by the inverse of the coefficient matrix to isolate X.

Step-by-step explanation:

To write the given system of equations as a matrix equation, we can represent the coefficients of the variables as a matrix, the variables as a column matrix, and the constants as another column matrix. The matrix equation can then be written as:

AX = B

where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix.

To solve the system using inverses, we can multiply both sides of the equation by the inverse of matrix A:

A-1AX = A-1B

Simplifying, we get:

X = A-1B

Substituting the given values into the equation and using matrix inverses, we can find the solution for X.

User Rajvijay
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