Concept:For a 2×2 determinant, acbd=ad−bc.Use this expansion to form an equation in m and solve it.Explanation:Given: m−2m+4m+1m−2=−27.Expand the determinant using the formula ad−bc.Here, a=m−2, b=m+1, c=m+4, d=m−2.So, (m−2)(m−2)−(m+1)(m+4)=−27.Simplify each product: (m−2)2=m2−4m+4.Also, (m+1)(m+4)=m2+5m+4.Substitute these into the equation: (m2−4m+4)−(m2+5m+4)=−27.The m2 terms and the constant 4 cancel, leaving −4m−5m=−27.Thus, −9m=−27.Divide both sides by −9: m=−9−27=3.Answer:m=3This corresponds to option B.