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

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

Answers (1)

Answer:  diag (0, -7, 17)

Hint:
diag=\begin{bmatrix} 1 &0 &0 \\ 0& 1&0 \\ 0& 0 & 1 \end{bmatrix}  using this formula in A, B, C and solve  A-2B.
Given: A = diag (2 -5 9), B = diag (1 1 -4) and C = diag (-6 3 4)
Here, we have to compute:A-2B.

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}

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

                 =\begin{bmatrix} 2 &0 &0 \\ 0& -5 &0 \\ 0 & 0 & 9 \end{bmatrix}-2\begin{bmatrix} 2 & 0 &0 \\ 0 & 2 &0 \\ 0 &0 & -8 \end{bmatrix}

                 =\begin{bmatrix} 2 -2&0 -0 &0 -0\\ 0- 0& -5-2 &0-0 \\ 0-0 & 0 -0& 9+8 \end{bmatrix}

                 =\begin{bmatrix} 0&0&0\\ 0& -7 &0 \\ 0 & 0 & 17 \end{bmatrix}

                 = diag (0, -7, 17)
Note: Here, C is not mandatory.

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