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  • Please Solve RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.1 Question 17 Subquestion (ii) Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.1 Question 17 Subquestion (ii) Maths Textbook Solution.

Answers (1)

Answer: \begin{bmatrix} 4 & 0 & 0\\ 0 &-3 &0 \\ 0& 0 &2 \end{bmatrix}

Here we have to give an example of diagonal matrix which is not scalar

Given:

Hint:  A diagonal matrix has only a_{11}\: a_{22}\: a_{33}   for a 3\times 3 matrix such that a_{11}\: a_{22}\: a_{33}   are equal or different and all other entries zero

Solution:  We know that a diagonal matrix has only a_{11}\: a_{22}\: a_{33}    for a 3\times 3 matrix such that a_{11}\: a_{22}\: a_{33}  are equal or different and all other entries zero. While scalar matrix has a_{11}= a_{22}= a_{33}= m    (say)

So, a diagonal matrix which is not scalar must have a_{11}\neq a_{22}\neq a_{33} and a_{ij}=0  for i\neq j .

Hence Required matrix = \begin{bmatrix} 4 & 0 & 0\\ 0 &-3 &0 \\ 0& 0 &2 \end{bmatrix}

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