Final answer:
To compute the inverse of a given matrix, we can use the formula A^-1 = (1/det(A)) * adj(A). For the matrix [2 1] [-1 4], the inverse is [4/9 -1/9] [1/9 2/9].
Step-by-step explanation:
Calculate the determinant of the matrix A, which is det(A) = 2*4 - (-1)*1 = 8 + 1 = 9.
The inverse of a 2x2 matrix A = [a b ; c d] is given by (1/det(A))*[d -b ; -c a]. So, apply this formula to the given matrix.
Thus, the inverse of matrix A is (1/9) * [4 -1 ; 1 2], which simplifies to [4/9 -1/9 ; 1/9 2/9].
To compute the inverse of a matrix, we can make use of the formula:
A-1 = (1/det(A)) * adj(A)
Where det(A) is the determinant of matrix A, and adj(A) is the adjugate of matrix A.
For the given matrix [2 1] [-1 4], the determinant is 2*4 - 1*(-1) = 9, and the adjugate is [4 -1] [1 2]. Plugging these values into the inverse formula, we get:
A-1 = (1/9) * [4 -1] [1 2]
Multiplying each element of the adjugate matrix by 1/9, we get:
[4/9 -1/9] [1/9 2/9]
Therefore, the inverse of the given matrix is [4/9 -1/9] [1/9 2/9].