CUET · MATHS · PYQ PAPER 2025
If \(\left[\begin{array}{ccc}a-b & 0 & 0 \\ 0 & b-c & 0 \\ 0 & 0 & c-2\end{array}\right]\) is a scalar matrix such that a + b + c = 0, then, which of the following are TRUE?
(A) a = 0
(B) b = 0
(C) a = 1
(D) c = 1
Choose the correct answer from the options given below:
- A (A) and (C) only
- B (B) and (D) only
- C (C) and (D) only
- D (A), (C) and (D) only
Answer & Solution
Correct Answer
(B) (B) and (D) only
Step-by-step Solution
Detailed explanation
\( a-b = b-c = c-2 \) \( b-c = c-2 \implies b = 2c-2 \) \( a-b = b-c \implies a = 2b-c = 2(2c-2)-c = 3c-4 \) \( a+b+c=0 \) \( (3c-4) + (2c-2) + c = 0 \) \( 6c-6 = 0 \implies c=1 \) \( b = 2(1)-2 = 0 \) \( a = 3(1)-4 = -1 \) Thus, \( a=-1, b=0, c=1 \). (A) \( a=0 \) is False. (B)…
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