THE INVERSE OF MATRIX
R=| 0 -1/4|
| 1 3/4|
=?
The formula you need is here:
http://www.mathcentre.ac.uk/students.php/all_subjects/matrices/matrix_arithmetic/resources/56
If I did it right, it's
3 1
-4 0
thanks
Judging by your other questions, you seem to be interested in just getting the answers, not understanding how to do the problem. In the future, I will not be responding you your posts where no work or thought is shown
To find the inverse of a matrix, we can use the formula:
A^(-1) = (1/det(A)) * adj(A)
where "A^(-1)" represents the inverse of matrix A, "det(A)" represents the determinant of matrix A, and "adj(A)" represents the adjugate of matrix A.
Let's calculate the inverse of matrix R step by step:
1. Calculate the determinant (det(R)):
The determinant of a 2x2 matrix can be found using the formula: det(R) = (a*d) - (b*c), where R = | a b | and | c d |.
In our case, R = | 0 -1/4 | where | 1 3/4 |
| 1 3/4 |
The determinant of R is: det(R) = (0*(3/4)) - (-1/4*1) = 1/4
2. Calculate the adjugate of R (adj(R)):
The adjugate of a 2x2 matrix can be found by swapping the positions of the elements of the main diagonal and changing the sign of the other two elements, giving the matrix: adj(R) = | d -b |.
| -c a |
In our case, adj(R) = | 3/4 1/4 |
| -1 0 |
3. Calculate the inverse of R (R^(-1)):
Using the formula mentioned earlier: R^(-1) = (1/det(R)) * adj(R).
In our case, R^(-1) = (1/(1/4)) * | 3/4 1/4 |
| -1 0 |
= 4 * | 3/4 1/4 |
| -1 0 |
= | 3 1 |
| -4 0 |
Therefore, the inverse of matrix R is: R^(-1) = | 3 1 |
| -4 0 |.