Let M,N and K be matrices of type 3×2,2×3 and 3×3 respectively, such that det (MN) =2 and det(K)=6. Then which of the following is the value of the det [(−3MN)TK−1]−1? a) −32.2 b)−133.2 c) 232 d)−324 e) −132

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Let M,N and K be matrices of type 3×2,2×3 and 3×3 respectively, such that det (MN) =2 and det(K)=6. Then which of the following is the value of the det [(−3MN)TK−1]−1?  a) −32.2 b)−133.2 c) 232 d)−324 e) −132

Aamina Herring · Accepted Answer

Step 1   Determinant properties help to find the determinant of the given matrix.   Determinant property for the multiples helps to do the required, which is defined as |k⋅A|%{n}=kn⋅|A|n.   Here k is the real number whereas A is the square matrix.   The determinant of the matrix is equal to the determinant of its transpose.  Step 2   Apply the determinant properties for the multiples to find the required answer.   Apply the determinant properties for the product of matrices, which is defined as |A⋅B|=|A|⋅|B|.   Put the values of the determinants in equation  (1) and solve.   det[(−3MN)TK−1]−1=(−3)−1(det(MN))T−1det(K)−1−1=−13(det(MN)T)−1det(K)…………………..(1)=−13(2)−1(6)=−13126=−1

Let M,N and K be matrices of type 3 \times

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