Show that the following matrices are skew symmetric: `[[0,e,f],[-e,0,g],[-f,-f,0]]`

Show that the following matrices are skew symmetric: [[0,1,-1],[-1,0,1],[1,-1,0]]

The matrix A=[{:(1,0,0),(0,2,0),(0,0,3):}] is: a) scalar matrix b) symmetric matrix c) skew symmetric matrix d) none f these

Consider the matrix A=[{:(0,-h,-g),(h,0,-f),(g,f, 0):}] STATEMENT-1 : Det A = 0 STATEMENT-2 :The value of the determinant of a skew symmetric matrix of odd order is always zero.

If A={:[(a,2,3),(b,c,4),(d,e,f)]:} is skew symmetric matrix, then find a,b,c,d,e,f.

Show that the function f(x) given by f(x)={((e^(1/x)-1)/(e^(1/x)+1), when x!=0), (0, when x=0):} is discontinuous at x=0 .

Show that f(x)=e^(1/x),x!=0 is decreasing function for all x!=0.

Show that f(x)=e^(1//x),\ \ x!=0 is a decreasing function for all x!=0 .

If A B C and DEF are two triangles such that A B C\ ~= F D E\ a n d\ A B=5c m ,\ /_B=40^0\ a n d\ /_A=80^0dot Then, which of the following is true? (a)D F=5c m ,\ /_F=60^0 (b) D E=5c m ,\ /_E=60^0 (c)D F=5\ c m ,\ /_E=60^0 (d) D E=5c m ,\ /_D=40^0

Two functions f & g have first & second derivatives at x=0 & satisfy the relations, f(0) = 2/(g(0)), f'(0)=2g'(0) = 4g(0), g"(0)= 5 f"(0)=6f(0) = 3 then-

Let f and g be function continuous in [a,b] and differentiable on [a,b] .If f(a)=f(b)=0 then show that there is a point c in (a,b) such that g'(c) f(c)+f'(c)=0 .