Answer:
To find the inverse of a 2x2 matrix, you can use the following formula:
If you have a matrix A:
| a b |
| c d |
The inverse of A, denoted as A⁻¹, can be found using the formula:
A⁻¹ = (1 / det(A)) * | d -b |
| -c a |
Where "det(A)" is the determinant of the matrix A.
In your case, you have the matrix:
A = | 4 12 |
| 1 10 |
1. Calculate the determinant of A:
det(A) = (4 * 10) - (12 * 1)
det(A) = 40 - 12
det(A) = 28
2. Calculate the inverse of A using the formula:
A⁻¹ = (1 / det(A)) * | 10 -12 |
| -1 4 |
3. Now, divide each element of A⁻¹ by 28:
a = 10 / 28 = 5/14
b = -12 / 28 = -3/7
c = -1 / 28 = -1/28
d = 4 / 28 = 1/7
So, the inverse of matrix A is:
A⁻¹ = | 5/14 -3/7 |
| -1/28 1/7 |
And the values for a, b, c, and d are as calculated above.
Explanation: