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  • Provide Solution For R.D.Sharma Maths Class 12 Chapter 4 Algebra of Matrices Exercise Multiple Choice Questions Question 12 Maths Textbook Solution.

Provide Solution For  R.D.Sharma Maths Class 12 Chapter 4 Algebra of Matrices Exercise Multiple Choice Questions Question 12 Maths Textbook Solution.

Answers (1)

Answer: The correct option is (A).

Given:A=\left[\begin{array}{lll} 1 & 2 & x \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right] \text { and } B=\left[\begin{array}{ccc} 1 & -2 & y \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right]

Solution: A B=\left[\begin{array}{lll} 1 & 2 & x \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right] \times\left[\begin{array}{ccc} 1 & -2 & y \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right]

                =\left[\begin{array}{ccc} 1+0+0 & -2+2+0 & y+0+x \\ 0+0+0 & 0+1+0 & 0+0+0 \\ 0+0+0 & 0+0+0 & 0+0+1 \end{array}\right]

=\left[\begin{array}{ccc} 1 & 0 & x+y \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right]

I_{3}=\left[\begin{array}{ccc} 1 & 0 & x+y \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right]=\left[\begin{array}{lll} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right]

Hence,

x + y = 0

So, the correct option is (A).

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