Final answer:
To find the inverse of a 2x2 matrix, calculate the determinant, find the adjugate, and divide by the determinant.
Step-by-step explanation:
To find the inverse of a 2x2 matrix, you need to follow certain steps. Given the matrix [ 0.4 -1.2 ] [ 0.3 0.6 ], calculate the determinant of the matrix, which is (0.4)(0.6) - (-1.2)(0.3) = 0.72 - (-0.36) = 1.08. Then find the adjugate of the matrix by swapping the diagonal elements and changing the sign of the off-diagonal elements, giving you [ 0.6 1.2 ] [ -0.3 0.4 ]. Finally, divide the adjugate matrix by the determinant, so the inverse is [ 0.6/1.08 1.2/1.08 ] [ -0.3/1.08 0.4/1.08 ] = [ 0.5556 1.1111 ] [ -0.2778 0.3704 ].