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  • Need solution for RD Sharma maths class 12 chapter Determinants exercise 5.1 question 2 subquestion (iv)

Need solution for RD Sharma maths class 12 chapter Determinants exercise 5.1 question 2 subquestion (iv)

Answers (1)

Answer:

a^{2}+b^{2}+c^{2}+d^{2}

Hint:

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

Given:

\begin{aligned} \left|\begin{array}{cc} \mathrm{a}+\mathrm{ib} & \mathrm{c}+\mathrm{id} \\ -\mathrm{c}+\mathrm{id} & \mathrm{a}-\mathrm{ib} \end{array}\right|\\ \end{aligned}

Solution:

\begin{aligned} &\begin{aligned} &\mathrm{D}=\mathrm{a}_{11} \times \mathrm{C}_{11}+\mathrm{a}_{21} \times \mathrm{C}_{21} \\ &\quad=\mathrm{a}+\mathrm{ib}(\mathrm{a}-\mathrm{ib})+\mathrm{c}+\mathrm{id}(-\mathrm{c}+\mathrm{id}) \\ &\quad=\mathrm{a}^{2}-\mathrm{i}^{2} \mathrm{~b}^{2}-\mathrm{i}^{2} \mathrm{~d}^{2}+\mathrm{c}^{2} \\ &\quad=\mathrm{a}^{2}+\mathrm{c}^{2}+\mathrm{b}^{2}+\mathrm{d}^{2} \end{aligned} \end{aligned}

Posted by

Gurleen Kaur

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