What is the inverse of a matrix?
An example of an AI chatbot conversation about finding the inverse of a matrix.
What is the inverse of a matrix?
The inverse of a matrix A is another matrix, denoted as A⁻¹, such that when multiplied together, they yield the identity matrix.
How do I calculate the inverse of a 2x2 matrix?
For a 2x2 matrix [[a, b], [c, d]], the inverse is given by (1/(ad-bc)) * [[d, -b], [-c, a]], provided that ad-bc is not zero.
What if the determinant is zero?
If the determinant is zero, the matrix does not have an inverse and is considered singular.
Can you show me an example?
Sure! For the matrix [[2, 3], [1, 4]], the determinant is (24 - 31) = 5, so the inverse is (1/5) * [[4, -3], [-1, 2]].
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