Statement 1: For a singular square matrix `A ,A B=A C B=Cdot` Statement 2; `|A|=0,t h e nA^(-1)` does not exist.

If A is a square matrix of order 3 such that |A|=2,t h e n|(a d jA^(-1))^(-1)| is ___________.

Let Aa n dB b e two independent events. Statement 1: If (A)=0. 3a n dP(Auu barB )=0. 8 ,t h e nP(B) is 2/7. Statement 2: P(E)=1-P(E),w h e r eE is any event.

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

Let B is an invertible square matrix and B is the adjoint of matrix A such that AB=B^(T) . Then

Statement 1: The inverse of singular matrix A=([a_(i j)])_(nxxn),w h e r ea_(i j)=0,igeqji sB=([a i j-1])_(nxxn)dot Statement 2: The inverse of singular square matrix does not exist.

Statement 1: A=[4 0 4 2 2 2 1 2 1]B^(-1)=[1 3 3 1 4 3 1 3 4] . Then (A B)^(-1) does not exist. Statement 2: Since |A|=0,(A B)^(-1)=B^(-1)A^(-1) is meaning-less.

Statement 1: If g(x) is a differentiable function, g(2)!=0,g(-2)!=0, and Rolles theorem is not applicable to f(x)=(x^2-4)/(g(x))in[-2,2],t h e ng(x) has at least one root in (-2,2)dot Statement 2: If f(a)=f(b),t h e ng(x) has at least one root in (-2,2)dot Statement 2: If f(a)=f(b), then Rolles theorem is applicable for x in (a , b)dot

Let Aa n dB be two independent events. Statement 1: If P(A)=0. 4a n dP(Auu barB )=0. 9 ,t h e nP(B)i s1//6. Statement 2: If Aa n dB are independent, then P(AnnB)=P(A)P(B)dot .

Statement 1: If vec A=2 hat i+3 hat j+6 hat k , vec B= hat i+ hat j-2 hat ka n d vec C= hat i+2 hat j+ hat k , then | vec Axx( vec Axx( vec Axx vec B)). vec C|=243 Statement 2: | vec Axx( vec Axx( vec Axx vec B)). vec C|=| vec A|^2|[ vec A vec B vec C]| a. Statement 1 and Statement 2 , both are true and Statement 2 is the correct explanation for Statement 1. b. Statement 1 and Statement 2 , both are true and Statement 2 is not the correct explanation for Statement 1. c. Statement 1 is true but Statement 2 is false. c. Statement 2 is true but Statement 1 is false.

Show that ("lim")_(xto0) (e^ (1/x)+1 / e^ (1/x)-1) does not exist