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  • Need solution for RD Sharma maths class 12 chapter Determinants exercise 5.1 question 6

Need solution for RD Sharma maths class 12 chapter Determinants exercise 5.1 question 6

Answers (1)

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Answer:

0

Hint:

Determinant matrix must be square (i.e. same number of rows and columns)

Given:

\left|\begin{array}{ccc} 0 & \sin \alpha & -\cos \alpha \\ -\sin \alpha & 0 & \sin \beta \\ \cos \alpha & -\sin \beta & 0 \end{array}\right|

Solution:

\begin{aligned} &\Delta=\mathrm{a}_{11} \mathrm{C}_{11}+\mathrm{a}_{21} \mathrm{C}_{21+} \mathrm{a}_{31} \mathrm{C}_{31}\\ &=(-1)^{1+1} 0\left(0+\sin ^{2} \beta\right)+(-1)^{1+2} \sin \alpha(0-\sin \beta \cos \alpha)+(-1)^{1+3}(-\cos \alpha)(\sin \alpha \sin \beta-0)\\ &=0\left(0+\sin ^{2} \beta\right)-\sin \alpha(0-\sin \beta \cos \alpha)-\cos \alpha(\sin \alpha \sin \beta-0)\\ &=\sin \alpha \sin \beta \cos \alpha-\cos \alpha \sin \alpha \sin \beta\\ &\Delta=0 \end{aligned}

 

 

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