Ques 1 and 2

Ques 1 and 2 3

Dear Student, 1) Here it is given a_{ij} = i + j (where' i' is the row number and' j' is the column number) A = [\begin{matrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{matrix}] \Rightarrow A = [\begin{matrix} 1 + 1 & 1 + 2 \\ 2 + 1 & 2 + 2 \end{matrix}] \Rightarrow A = [\begin{matrix} 2 & 3 \\ 3 & 4 \end{matrix}] 2) . [\begin{matrix} x + y & a + b \\ a - b & 2 x - 3 y \end{matrix}] = [\begin{matrix} 5 & - 1 \\ 3 & - 5 \end{matrix}] Every element of a matrix is equal to the corresponding elements on the right side matrix . So, x + y = 5 \Rightarrow x = 5 - y . . . . . . . . . . . . . (i) and 2 x - 3 y = - 5 . . . . . . . . (ii) from equation (i) put the value of x in equation (ii) \Rightarrow 2 x - 3 y = - 5 \Rightarrow 2 (5 - y) - 3 y = - 5 \Rightarrow 10 - 2 y - 3 y = - 5 \Rightarrow 10 - 5 y = - 5 \Rightarrow 5 y = 15 \Rightarrow y = 3 Now put the value of' y' in equation (i) x = 5 - y \Rightarrow x = 5 - 3 \Rightarrow x = 2 Now, For' a' and' b' a + b = - 1 \Rightarrow a = - 1 - b . . . . (iii) and a - b = 3 . . . . . . . . . (iv) Now put the value of a from equation (iii) a - b = 3 \Rightarrow (- 1 - b) - b = 3 \Rightarrow - 1 - 2 b = 3 \Rightarrow 2 b = - 4 \Rightarrow b = - 2 Now put the value of b in equation (iii) a = - 1 - b \Rightarrow a = - 1 - (- 2) \Rightarrow a = - 1 + 2 \Rightarrow a = 1 Regards .