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  • Provide solution for RD Sharma maths class 12 chapter 4 Algebra of Matrices exercise Fill in the blank question 10

Provide solution for RD Sharma maths class 12 chapter 4 Algebra of Matrices exercise Fill in the blank question 10

Answers (1)

Answer:

A2B = diag(-4,3,18)

 Hint:

Use the concept of diagonal matrix.

 Given:

 A = diag(2,-1, 3) and B = diag(-1, 3, 2)

 Solution:

\begin{aligned} &A^{2}=\left[\begin{array}{ccc} 2 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 3 \end{array}\right] \times\left[\begin{array}{ccc} 2 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 3 \end{array}\right]=\left[\begin{array}{lll} 4 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 9 \end{array}\right] \\ &A^{2} \times B=\left[\begin{array}{lll} 4 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 9 \end{array}\right] \times\left[\begin{array}{ccc} -1 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 2 \end{array}\right]=\left[\begin{array}{ccc} -4 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 16 \end{array}\right] \end{aligned}

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Gurleen Kaur

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