Question

Write a formula for the inverse of a 2 times 2 matrix.

Answer 1

To find the inverse of a 2x2 matrix, calculate the determinant of the matrix and then apply the inverse formula.

Step-by-step explanation:

To find the inverse of a 2x2 matrix, follow these steps:

1. Let's say the matrix is A = [a b; c d].
2. Find the determinant of A, denoted as det(A), which is calculated as det(A) = ad - bc.
3. The inverse of A is given by A^-1 = (1/det(A)) * [d -b; -c a].

For example, consider the matrix A = [2 3; 4 5]. The determinant is det(A) = (2 * 5) - (3 * 4) = 10 - 12 = -2. Therefore, the inverse of A is A^-1 = (1/-2) * [5 -3; -4 2] = [-5/2 3/2; 2 -1].