Math Problem Statement
Consider the following system of linear equations: 2x1+2x2+6x3 = −14 −x1+4x2+2x3 = −13 3x1+7x3 = −10
Let A be the coefficient matrix and X the solution matrix to the system. Solve the system by first computing A−1 and then using it to find X.
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Solution
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Matrix Inversion
Systems of Linear Equations
Formulas
Matrix form of system: A * X = B
Inverse of a matrix: A^(-1)
Solution to system: X = A^(-1) * B
Theorems
Inverse Matrix Theorem
Properties of Matrices
Suitable Grade Level
Undergraduate Level or Advanced High School (Grades 11-12)