Write the minors and cofactors of each element of the first column of the matrices and hence evaluate the determinant in each case:

$$A=\begin{bmatrix}1 &-3&2 \\[0.3em] 4 & -1&2 \\[0.3em] 3 &5&2 \\[0.3em] \end{bmatrix}$$

Asked by Aaryan | 1 year ago |  67

Solution :-

Let Mij and Cij represents the minor and co–factor of an element, where i and j represent the row and column. The minor of the matrix can be obtained for a particular element by removing the row and column where the element is present. Then finding the absolute value of the matrix newly formed.

Also, Cij = (–1)i+j × Mij

$$M_{11}=-12$$

$$M_{21}=-16$$

M31 = –3 × 2 – (–1) × 2

M31 = –4

C11 = (–1)1+1 × M11

= 1 × –12

= –12

C21 = (–1)2+1 × M21

= –1 × –16

= 16

C31 = (–1)3+1 × M31

= 1 × –4

= –4

Now expanding along the first column we get

|A| = a11 × C11 + a21× C21+ a31× C31

= 1× (–12) + 4 × 16 + 3× (–4)

= –12 + 64 –12

= 40

Answered by Sakshi | 1 year ago

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