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Inverse Matrices (2 x 2)

Inverse Matrices (2 x 2). How to find the inverse of a 2x2 matrix. Inverse of a number. When we are talking about our natural numbers, the inverse of a number is it’s reciprocal. When we multiply a number by it’s inverse we get 1. For example:. Inverse of a matrix.

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Inverse Matrices (2 x 2)

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  1. Inverse Matrices (2 x 2) How to find the inverse of a 2x2 matrix

  2. Inverse of a number When we are talking about our natural numbers, the inverse of a number is it’s reciprocal. When we multiply a number by it’s inverse we get 1. For example:

  3. Inverse of a matrix What do you think we would get if we multiplied a matrix by it’s inverse? Try it on your calculator. A matrix multiplied by its inverse always gives us an identity matrix.

  4. Inverse of a matrix Not all matrices have an inverse. If the determinant of a matrix is 0, then it has no inverse and is said to be SINGULAR. All others are said to be NON-SINGULAR

  5. Inverse of a matrix Which of these have an inverse?

  6. Finding Inverses 2x2 Let A-1 = So AA-1 = I Multiplying out gives.. Can you solve these to work out A-1?

  7. Finding Inverses 2x2 There is an alternative method. ad-bc represents det(A). What would happen if this was zero? a d b -b • In words: • Take the original matrix. • Switch a and d. • Change the signs of b and c. • Multiply the new matrix by 1 over the determinant of the original matrix. c -c d a

  8. Finding Inverses 2x2 Example: Find the inverse of A. =

  9. Finding Inverses 2x2

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