A scalar matrix is a special type of diagonal matrix where all diagonal elements are equal. For example:
\[ A = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end{bmatrix} \]is a scalar matrix and also a diagonal matrix. However, the reason given, "In a diagonal matrix, all the diagonal elements are 0," is incorrect because diagonal matrices can have any value along their diagonal elements, not necessarily 0.
Final Answer: \( \boxed{[(C)] \text{Assertion (A) is true, but Reason (R) is false.}} \)Show that \( R \) is an equivalence relation. Also, write the equivalence class \([2]\).
List-I | List-II |
(A) Absolute maximum value | (I) 3 |
(B) Absolute minimum value | (II) 0 |
(C) Point of maxima | (III) -5 |
(D) Point of minima | (IV) 4 |
A battery of emf \( E \) and internal resistance \( r \) is connected to a rheostat. When a current of 2A is drawn from the battery, the potential difference across the rheostat is 5V. The potential difference becomes 4V when a current of 4A is drawn from the battery. Calculate the value of \( E \) and \( r \).