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  • Please Solve RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.2 Question 12 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.2 Question 12 Maths Textbook Solution.

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Answer:  C = \begin{bmatrix} -24 &-10 \\ -28 & -38 \end{bmatrix}

Hint: Null matrix is \begin{bmatrix} 0 &0\\ 0 & 0 \end{bmatrix}

Given:   A =\begin{bmatrix} 9 &1 \\ 7 & 8 \end{bmatrix} , B =\begin{bmatrix} 1 & 5\\ 7 & 12 \end{bmatrix}, 5A + 3B + 2C = 0

Here, we have to compute C.

Solution:

5A + 3B + 2C = \begin{bmatrix} 0 &0 \\ 0 & 0 \end{bmatrix}

5\begin{bmatrix} 9 & 1\\ 7 & 8 \end{bmatrix} + 3\begin{bmatrix} 1 & 5\\ 7 & 12 \end{bmatrix} + 2C = \begin{bmatrix} 0 &0 \\ 0&0 \end{bmatrix}

\begin{bmatrix} 45 & 5\\ 35 & 40 \end{bmatrix} + \begin{bmatrix} 3 & 15\\ 21 & 36 \end{bmatrix} + 2C = \begin{bmatrix} 0 &0 \\ 0&0 \end{bmatrix}

\begin{bmatrix} 45+3 & 5+15\\ 35+21 & 40+36 \end{bmatrix} + 2C = \begin{bmatrix} 0 &0 \\ 0&0 \end{bmatrix}

\begin{bmatrix} 48 & 20\\ 56 & 76 \end{bmatrix} + 2C = \begin{bmatrix} 0 &0 \\ 0&0 \end{bmatrix}

2C = \begin{bmatrix} 0 &0 \\ 0&0 \end{bmatrix}-\begin{bmatrix} 48 & 20\\ 56 & 76 \end{bmatrix}

2C = \begin{bmatrix} -48 & -20\\ -56 & -76 \end{bmatrix}

C =\frac{1}{2}\begin{bmatrix} -48 & -20\\ -56 & -76 \end{bmatrix}

C = \begin{bmatrix} -24 &-10 \\ -28 & -38 \end{bmatrix} 

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