Maths-
General
Easy

Question

Suppose A equals open square brackets table row 1 0 row 0 cell negative 1 end cell end table close square brackets, B equals open square brackets table row 2 0 row 0 cell negative 2 end cell end table close square brackets let x be a 2×2 matrix such that X to the power of straight primeAX = B
Statement-I : X is non singular & |x| = ±2
Statement-II : X is a singular matrix

  1. If both (A) and (R) are true, and (R) is the correct explanation of (A).    
  2. If both (A) and (R) are true but (R) is not the correct explanation of (A).    
  3. If (A) is true but (R) is false.    
  4. If (A) is false but (R) is true.    

The correct answer is: If (A) is true but (R) is false.


    If X = 0 then X to the power of straight primeAX = 0  B = 0 (contradiction)
    Let |X| = a, then |X to the power of straight prime|= a
    therefore|X to the power of straight primeAX| = |B|
    a (–1)a = –4 not stretchy rightwards double arrow a = ± 2
    As |x| not equal to 0, X cannot be a singular matrix
    thereforestatement :I is true & 2 is false.

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