Statement 1: if `D=`diag`[d_1, d_2, ,d_n]`,then `D^(-1)=`diag`[d_1^(-1),d_2^(-1),...,d_n^(-1)]` Statement 2: if `D=`diag`[d_1, d_2, ,d_n]`,then `D^n=`diag`[d_1^n,d_2^n,...,d_n^n]`

If D=d i ag[d_1, d_2, d_n] , then prove that f(D)=d i ag[f(d_1),f(d_2), ,f(d_n)],w h e r ef(x) is a polynomial with scalar coefficient.

If the S.D of x_(1),x_(2),x_(3),........x_(n) is 6, then the S.D of -x_(1),-x_(2),.......,-x_(n) is

Statement 1: if a ,b ,c ,d are real numbers and A=[a b c d]a n dA^3=O ,t h e nA^2=Odot Statement 2: For matrix A=[a b c d] we have A^2=(a+d)A+(a d-b c)I=Odot

sum_(k=1)^ook(1-1/n)^(k-1)= a. n(n-1) b. n(n+1) c. n^2 d. (n+1)^2

If k in R_ot h e ndet{a d j(k I_n)} is equal to K^(n-1) b. K^(n(n-1)) c. K^n d. k

If (sin^(-1)x+sin^(-1)w)(sin^(-1)y+sin^(-1)z)=pi^2, then D=|x^(N_1)y^(N_3)z^(N_3)w^(N_4)|(N_1,N_2,N_3,N_4 in N)

if D_(k) = |{:( 1,,n,,n),(2k,,n^(2)+n+1 ,,n^(2)+n),(2k-1,,n^(2),,n^(2)+n+1):}|" and " Sigma_(k=1)^(n) D_(k)=56 then n equals

If roots of an equation x^n-1=0 are 1,a_1,a_2,........,a_(n-1) then the value of (1-a_1)(1-a_2)(1-a_3)........(1-a_(n-1)) will be (a) n (b) n^2 (c) n^n (d) 0

If the midpoints of the sides of a triangle are (2,1),(-1,-3),a n d(4,5), then find the coordinates of its vertices.

Let {D_1, D_2, D_3 ,D_n} be the set of third order determinant that can be made with the distinct non-zero real numbers a_1, a_2, a_qdot Then sum_(i=1)^n D_i=1 b. sum_(i=1)^n D_i=0 c. D_i-D_j ,AAi ,j d. none of these