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Inverses

Inverses. Definition. For any two matrices A and B, if AB = BA = I , then A and B are called inverse matrices The symbols A -1 denotes the inverse of matrix A If A = and det A ≠ 0 then A -1 = If det A = 0, then A has no inverse. Example 1. Find A -1 if A =

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Inverses

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  1. Inverses

  2. Definition • For any two matrices A and B, if AB = BA = I, then A and B are called inverse matrices • The symbols A-1 denotes the inverse of matrix A • If A = and det A ≠ 0 then A-1 = • If det A = 0, then A has no inverse

  3. Example 1 • Find A-1 if A = • First find the determinant • Interchange a and d, replace both b and c with their opposites and then multiply the resulting by 1/det A

  4. Answer to Example 1

  5. Practice • Page 792 WE #1 – 8

  6. How to convert a SOE to a Matrix • Covert the SOE to a matrix

  7. Practice • Page 792 WE #9 – 16

  8. Using matrices to solve SOE • Use matrices to solve this system: • Write the SOE as a matrix equation • Find the determinant of the coefficient matrix • If equal to zero no unique solution • Find the inverse of the coefficient matrix • Multiply the inverse matrix by the coefficient matrix and the solutions matrix • The solution of the equation AX = B is X = A-1B

  9. Practice • Page 792 WE #9 – 16

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