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  • Provide solution for RD Sharma maths class 12 chapter 4 Algebra of Matrices exercise Fill in the blank question 6

Provide solution for RD Sharma maths class 12 chapter 4 Algebra of Matrices exercise Fill in the blank question 6

Answers (1)

Answer:

x = ±1

 Hint:

Use the basic concept of matrix multiplication

 Given:

A=\left[\begin{array}{cc} x & 1 \\ -1 & -x \end{array}\right] \text { and } A^{2}=0 \text { then } x=0

Solution:

\begin{aligned} &A \times A=\left[\begin{array}{cc} x & 1 \\ -1 & -x \end{array}\right] \times\left[\begin{array}{cc} x & 1 \\ -1 & -x \end{array}\right] \\ &=\left[\begin{array}{cc} x^{2}+(-1) & x+(-x) \\ -x+x & -1+x^{2} \end{array}\right] \\ &=\left[\begin{array}{cc} x^{2}-1 & 0 \\ 0 & x^{2}-1 \end{array}\right] \end{aligned}

\begin{aligned} &\text { Since, } A^{2}=0 \\ &{\left[\begin{array}{cc} x^{2}-1 & 0 \\ 0 & x^{2}-1 \end{array}\right]=\left[\begin{array}{ll} 0 & 0 \\ 0 & 0 \end{array}\right]} \\ &x^{2}-1=0 \\ &x^{2}=1 \\ &x=\pm 1 \end{aligned}

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Gurleen Kaur

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