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Fundamentals of Engineering Analysis EGR 1302 The Inverse Matrix

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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  1. Fundamentals of Engineering Analysis EGR 1302 The Inverse Matrix

  2. 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

  3. Sum of Products The same equation can represent any Order. Solving Systems of Linear Equations

  4. ( ) ( ) Solving this System for x1, x2 Becomes Subtract

  5. A new Matrix “C” Solving this System for x1, x2 (cont.) factor out the denominator Sum of Products

  6. The Solution to We now have a solution for the Inverse of a 2x2 Matrix

  7. The Determinant The Determinant of A =

  8. 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

  9. If there is no solution Stay Tuned! Review of the Solution to a 2x2 System Is solved by

  10. A Numerical Example Becomes

  11. Questions?

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