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Understanding the Inverse of a 2x2 Matrix

Learn how to calculate the inverse of a 2x2 matrix using specific rules and examples. Understand the method and significance of matrix inversion in mathematics.

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Understanding the Inverse of a 2x2 Matrix

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  1. Matrices - Inverse of a 2  2 Matrix • To find the inverse of a 2  2 matrix, use the following pattern. • Let matrix A be given by ... • Then the inverse of A is given by ...

  2. Negative of each entry. Switch entries. Matrices - Inverse of a 2  2 Matrix • Example 1: • Find the inverse of • matrix A where ... Slide 2

  3. Matrices - Inverse of a 2  2 Matrix • As a check, multiply A and A-1 ... • Since the result of the product is the identity matrix, the matrices are inverses. Slide 3

  4. Matrices - Inverse of a 2  2 Matrix • Example 2: • Find the inverse of • matrix B where ... • But this is impossible since the denominator is zero! • Thus, B-1 does not exist. Slide 4

  5. Matrices - Inverse of a 2  2 Matrix END OF PRESENTATION Click to rerun the slideshow.

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