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  • Explain solution for RD Sharma Class 12 Chapter 5 Determinants Exercise Very short Answers Question 18 maths textbook solution.

Explain solution for RD Sharma Class 12 Chapter 5 Determinants Exercise Very short Answers Question 18 maths textbook solution.

Answers (1)

Answer : 5

Hint: Here we use basic concept of determinant of matrix

Given : A=\left[a_{i j}\right] \text { is a square matrix of order } 3 \times 3 \text { and } \mathrm{c}_{i j} \text { is cofactor of } a_{i j} \text { then }

Solution :

Here \sum_{i=1}^{n} a_{i j} c_{i j}=|A| \text { and } \sum_{j=1}^{n} a_{i j} c_{i j}=|A|

\rightarrow|A|=5 \text { and matrix } \mathrm{A} \text { is of order } 3 \times 3

\rightarrow Since we know that

a_{13} c_{13}+a_{23} c_{23}+a_{33} c_{33} represent expansion of A along third column

\begin{aligned} &\rightarrow \mathrm{So}, a_{13} c_{13}+a_{23} c_{23}+a_{33} c_{33}=|A| \\ &\rightarrow \mathrm{So}, a_{13} c_{13}+a_{23} c_{23}+a_{33} c_{33}=5 \end{aligned}

 

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