Matrix Ar=[r r -1 r -1 r] ; r=1,2,3, ldots . If displaystyle∑r=1100|Ar|, then K = ldots ldots ldots ldots(|Ar|=det(Ar))

Question

Matrix Ar=[r r -1 r -1 r] ; r=1,2,3, ldots . If displaystyle∑r=1100|Ar|, then K = ldots ldots ldots ldots(|Ar|=det(Ar)) (A) 2 (B) 6 (C) 4 (D) 8

Tardigrade Admin · Accepted Answer

|Ar|=2 r -1 displaystyle∑r=1100(2 r -1)=1+3+ ldots+199=10000=10k / 2 ⇒ (k/2)=4 ⇒ k =8

Q. Matrix $A_{r} = [r r r - 1 - 1 r]; r = 1, 2, 3, \dots .$ If $r = 1 \sum 100 ∣ A_{r} ∣$ , then $K = \dots\dots\dots\dots (∣ A_{r} ∣ = d e t (A_{r}))$