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Question
If Δ = `|(a_11,a_12,a_13),(a_21,a_22,a_23),(a_31,a_32,a_33)|` and Aij is Cofactors of aij, then the value of Δ is given by ______.
Options
a11A31 + a12A32 + a13A33
a11A11 + a12A21 + a13A31
a21A11 + a22A12 + a23A13
a11A11 + a21A21 + a31A31
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Solution
If Δ = `|(a_11,a_12,a_13),(a_21,a_22,a_23),(a_31,a_32,a_33)|` and Aij is Cofactors of aij, then the value of Δ is given by a11A11 + a21A21 + a31A31.
Explanation:
∆ = The sum of the product of the elements of a row or column and their corresponding super-parts.
C1 = Components of a column (a11, a21, a31)
Cofactors = A11, A21, A31
⇒ ∆ = a11A11 + a21A21 + a31A31
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