Math Problem Statement
Solve the system of equations using x = A−1b: 2x1 + x2 + 5x3 + x4 = 5, x1 + x2 − 3x3 − 4x4 = −1, 3x1 + 6x2 − 2x3 + x4 = 8, 2x1 + 2x2 + 2x3 − 3x4 = 2
Solution
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Matrix Inversion
Systems of Linear Equations
Formulas
Matrix equation: x = A^{-1}b
Inverse of a matrix formula
Determinant of a matrix
Theorems
Matrix Inverse Theorem
Cramer's Rule (related)
Determinant Theorem
Suitable Grade Level
Undergraduate (or advanced high school, Grades 11-12)