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  • Please Solve RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.2 Question 5 Subquestion (ii) Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.2 Question 5 Subquestion (ii) Maths Textbook Solution.

Answers (1)

Answer: diag (-9 14 -18)

Hint:

diag= \begin{bmatrix} 1 & 0 & 0\\ 0 & 1& 0\\ 0 & 0 & 1 \end{bmatrix}  using this formula in A, B, C and solve B + C -2A.

Given:A = diag (2 -5 9), B = diag (1 1 -4) and\: C = diag (-6 3 4)

Here, we have to compute: B + C -2A.

Solution:
A=\begin{bmatrix} 2 &0 &0 \\ 0& -5 &0 \\ 0 & 0 & 9 \end{bmatrix},B=\begin{bmatrix} 1 & 0 &0 \\ 0 & 1 &0 \\ 0 &0 & -4 \end{bmatrix},C= \begin{bmatrix} -6 &0 & 0\\ 0 & 3 &0 \\ 0 & 0 & 4 \end{bmatrix}

B+C-2A=\begin{bmatrix} 1 &0 &0 \\ 0& 1 &0 \\ 0 & 0 & -4 \end{bmatrix}+\begin{bmatrix} -6 & 0 &0 \\ 0 & 3 &0 \\ 0 &0 & 4 \end{bmatrix}-2 \begin{bmatrix} 2 &0 & 0\\ 0 & -5 &0 \\ 0 & 0 & 9 \end{bmatrix}

                         =\begin{bmatrix} 1 &0 &0 \\ 0& 1 &0 \\ 0 & 0 & -4 \end{bmatrix}+\begin{bmatrix} -6 & 0 &0 \\ 0 & 3 &0 \\ 0 &0 & 4 \end{bmatrix}-\begin{bmatrix} 4 &0 & 0\\ 0 & -10 &0 \\ 0 & 0 & 18 \end{bmatrix}

                          =\begin{bmatrix} 1-6-4 &0+0-0 &0+0-0 \\ 0+0-0& 1+3+10 &0+0-0 \\ 0 +0-0& 0+0-0 & -4+4-18 \end{bmatrix}

                           =\begin{bmatrix} -9 &0 &0\\ 0& 14 &0 \\ 0 & 0 & -18 \end{bmatrix}
                          = diag (-9\: \ 14 -18)

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