What is the inverse of matrix C, to the nearest hundredth?
10 -6
C=
-12 2
The inverse is
(-1 -3 )
(-6 -5 ) / 26
I'll let you do the divisions
To find the inverse of a matrix, you need to follow these steps:
1. Calculate the determinant of the matrix C. The determinant of a 2x2 matrix is calculated using the formula:
determinant(C) = (a*d) - (b*c), where C = [a b; c d]
In this case, the determinant of C would be:
determinant(C) = (10 * 2) - (-6 * -12) = 20 - 72 = -52
2. Check if the matrix is invertible. If the determinant is nonzero (not equal to 0), then the matrix is invertible. In this case, since the determinant is -52 which is nonzero, the matrix C is invertible.
3. Calculate the adjugate of the matrix C. The adjugate matrix is obtained by swapping the positions of the elements in the main diagonal (10 and 2) and changing the sign of the other two elements (-6 and -12).
Adjugate(C) = [2 6; 12 10]
4. Calculate the inverse matrix by dividing each element of the adjugate matrix by the determinant of the original matrix C.
inverse(C) = (1/determinant(C)) * Adjugate(C)
inverse(C) = (1/-52) * [2 6; 12 10] = [-2/52 -6/52; -12/52 -10/52]
5. Finally, simplify the elements of the inverse matrix to the nearest hundredth:
inverse(C) ≈ [-0.04 -0.12; -0.23 -0.19]
So, the inverse of matrix C, to the nearest hundredth, is:
[-0.04 -0.12;
-0.23 -0.19]