If `A=[(0,-1,2),(1,0,3),(-2,-3,0)], then A+2A^t` equals (A) A (B) `-A^t` (C) `A^t` (D) `2A^2`

If A=1/3[(1,2,2),(2,1,-2),(x,2,y)] satisfies A^T A=I , then x+y= (a) 3 (b) 0 (c) -3 (d) 1

If A=[(1,-1) ,(2 ,3)],B=[(2, 1), (1, 0)],p rove t h a t (A+B)^2!=A^2+2A B+B^2

Consider the matrices A=[(4,6,-1),(3,0,2),(1,-2,5)], B=[(2,4),(0,1),(-1,2)], C=[(3),(1),(2)] Which of the following are defined? (a) (A B)^t C (b) C^T C(A B)^T (c) C^T A B (d) A^T A B B^T C

Let A=[(2,-3),(-7, 5)] and B=[(1, 0),( 2,-4)] , verify that (2A)^T=2A^T (ii) (A+B)^T=A^T+B^T (iii) (A-B)^T=A^T-B^T (iv) (A B)^T=B^T\ A^T

f(x) = int_(x)^(x^(2))(e^(t))/(t)dt , then f'(t) is equal to : (a) 0 (b) 2e (c) 2e^2 -2 (d) e^2-e

If x=(1+t)/(t^3),y=3/(2t^2)+2/t , then x((dy)/(dx))^3-(dy)/(dx) is equal to (a) 0 (b) -1 (c) 1 (d) 2

.If A=[[1,4,7],[2,5,8]] and B=[[-3,4,0],[4,-2,-1]] then show that (A+B)^T=A^T+B^T

If the straighat lines x=1+s,y=-3-lamdas,z=1+lamdas and x=t/2,y=1+t,z=2-t with parameters s and t respectively, are coplanar, then lamda equals (A) -1/2 (B) -1 (C) -2 (D) 0

If x=a t^2,y=2a t , then (d^2y)/(dx^2) is equal to (a) -1/(t^2) (b) 1/(2a t^2) (c) -1/(t^3) (d) 1/(2a t^3)

Let A=int_0^1(e^t)/(t+1)dt , then the value of (int_0^1t e^t^2)/(t^2+1)dt A^2 (b) 1/2A (c) 2A (d) 1/2A^2