1) The rank of the matrix [−1252−4a−41−2a+1] is A) 1 if a = 6 B) 2 if a = 1 C) 3 if a = 2 D) 1 if a = 4 Answer: Option BExplanation:Let A=[−1252−4a−41−2a+1]∼[−12500a+600a+6] [R2 → R2 + 2R1, R3 → R3 +R1] Clearly rank of A is 1 if a = -6 Also, for a= 1, | A | = |−1252−4−31−22|=0 and |25−4−3|=−6+20=14≠0 .'. rank of A is 2 if a = 1