How to use this applet:
Enter a matrix in the four boxes on the right. Click Invert Matrix! to invert the matrix you entered. Click Invert
Answer to invert the answer of the original inversion.
Notes on the maths used in the applet:
The Leaving Certificate Higher Level maths course requires that students can
invert 2X2 matries using a formula. The inverse of a matrix, A, is written A-1
and is defined as:
The formula for inverting a 2X2 matrix is:
The mathematical operations involved are not too difficult, and so remembering
the formula correctly is important:
| 1. Swap the elements in the leading diagonal: |
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| 2. Multiply the elements in the other diagonal by -1 - i.e.
change their sign: |
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| 3. Then multiply by the inverse determinant of the matrix
-- the determinant of a 2X2 matrix is (ad - bc): |
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Knowing how to invert matrices is essential for solving matrix equations. An
equation such as:
where:
and you are asked to find B in matrix form, is solvable only using matrix inversion.
Solving is done by pre-multiplying each matrix by C-1 resulting in:
Simplyfing gives:
which can be solved easily using Matrix Inversion.
