#### Please Solve RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.1 Question 4 Subquestion (ii) Maths Textbook Solution.

Answer: $A= \begin{bmatrix} 1 &0 &-1 \\ 3& 2& 1 \end{bmatrix}$
Given: Here given that matrix of order $2\times 3$
$A= \left [ a_{ij} \right ]_{2\times 3}$
Here we have to construct $2\times 3$ matrix as $a_{ij}= 2i-j$
Hint: We have to construct the matrix according to the question
Solution:   Let $A= \left [ a_{ij} \right ]_{2\times 3}$
So, the elements in a $2\times 3$ matrix are $a_{11},a_{12},a_{13},a_{21},a_{22},a_{23}$
$A= \begin{bmatrix} a_{11} & a_{12} &a_{13} \\ a_{21} & a_{22} & a_{23} \end{bmatrix}$
$\! \! \! \! \! \! \! \! \! a_{11}= 2\times 1-1= 2-1= 1\\a_{12}= 2\times 1-2= 2-2= 0\\a_{13}= 2\times 1- 3= 2-3= -1$            $\! \! \! \! \! \! \! \! \! a_{21}= 2\times 2-1= 4-1= 3\\a_{22}= 2\times 2-2= 4-2= 2\\a_{23}= 2\times 2- 3= 4-3= 1$
Substituting these values in Matrix $A$, we get
$A= \begin{bmatrix} 1 &0 &-1 \\ 3& 2& 1 \end{bmatrix}$
Hence this is the required answer.