Final answer:
To find the inverse of the coefficient matrix of the given linear equations, calculate the determinant, find the adjugate matrix, and then multiply each element of the adjugate matrix by the reciprocal of the determinant.
Step-by-step explanation:
The student has presented two linear equations:
- 0.3x + 0.3y = -1.2
- 0.5x - 0.2y = 3.6
To find the inverse of the coefficient matrix, we first need to write down the coefficient matrix:
A = [[0.3, 0.3], [0.5, -0.2]]
The inverse of matrix A can be calculated using the formula:
A-1 = 1/det(A) * adj(A)
Where det(A) is the determinant of A and adj(A) is the adjugate of A. The determinant is calculated as:
det(A) = 0.3*(-0.2) - 0.3*0.5 = -0.06 - 0.15 = -0.21
The adjugate of A is:
adj(A) = [[ -0.2, -0.3], [ -0.5, 0.3]]
Thus, the inverse matrix is:
A-1 = 1/(-0.21) * [[ -0.2, -0.3], [ -0.5, 0.3]]
Finally, multiply each element of the adjugate matrix by 1/(-0.21) to find A-1.