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

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

Answers (1)

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Answer: diag (37 -22 -14)

Hint:  using this formula inA, B, C and solve 2A + 3B - 5C.

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

Here, we have to compute:2A + 3B - 5C.

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}

2A+3B-5C=2\begin{bmatrix} 2 &0 &0 \\ 0& -5 &0 \\ 0 & 0 & 9 \end{bmatrix}+3\begin{bmatrix} 1 & 0 &0 \\ 0 & 1 &0 \\ 0 &0 & -4 \end{bmatrix}-5 \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}+3\begin{bmatrix} 3 & 0 &0 \\ 0 & 3 &0 \\ 0 &0 & -12 \end{bmatrix}-5 \begin{bmatrix} -30 &0 & 0\\ 0 & 15 &0 \\ 0 & 0 & 20 \end{bmatrix}

                                 =\begin{bmatrix} 4+3+30 &0+0-0 &0+0-0 \\ 0+0-0& -10+3-15 &0+0-0 \\ 0+0-0 & 0+0-0 & 18-12-20 \end{bmatrix}

                                 =\begin{bmatrix} 37 &0 &0\\ 0& -22 &0\\ 0 & 0 & -14 \end{bmatrix}

                                 = diag (37 -22 -14)
               

                         

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