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Fundamentals of Engineering Analysis EGR 1302 The Inverse Matrix. in Algebra, the equivalent is. Solving Systems of Linear Equations. The Inverse Matrix. A nxn and B nxn are Square Matrices of the same Order. A * B = I n. B * A = I n. B is called “The Inverse of A”. B = A -1.

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## Fundamentals of Engineering Analysis EGR 1302 The Inverse Matrix

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**Fundamentals of Engineering Analysis**EGR 1302 The Inverse Matrix**in Algebra, the equivalent is**Solving Systems of Linear Equations The Inverse Matrix Anxn and Bnxn are Square Matrices of the same Order. A * B = In B * A = In B is called “The Inverse of A” B = A-1 A * A-1 = I**Sum of Products**The same equation can represent any Order. Solving Systems of Linear Equations**( )**( ) Solving this System for x1, x2 Becomes Subtract**A new Matrix “C”**Solving this System for x1, x2 (cont.) factor out the denominator Sum of Products**The Solution to**We now have a solution for the Inverse of a 2x2 Matrix**The Determinant**The Determinant of A =**Rules for Finding the Inverse of a 2x2 Matrix**Rule 1: Swap the Main Diagonal Rule 2: Change Signs on the Back Diagonal Rule 3: Divide by the Determinant**If there is no solution**Stay Tuned! Review of the Solution to a 2x2 System Is solved by**A Numerical Example**Becomes

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