Revision2_23MA1002

From the following partial differential equations, the separable

equation is -------

• p+q=pq

• p -x = q -y

• z=px+qy+pq

• p+q+x+y=z

Identify the Clairaut's equation from the following partial differential

equations.

• z=px+qy+pq

• z=px+qz+p+q

• z=pz+qy+p-q

• z=p+qy+pq

• z=g(y)+h(x)

• z=g(y)-h(x)

• z=g(y)*h(x)

• z=g(y)/h(x)

Identify a set of multiplier to solve the Lagrange's equation: x(y-z)

p+y(z-x)q=z(x-y).

• (1/x,1/y²,1/z)

• (1/x²,1/y,1/z)

• (x,y,z)

• (1/x,1/y,1/z)

If a linear transformation T: V₃ → V₃ is defined as T(x,y,z ) = (0,0,z)

then, find the value of T(2,3,4) .

• (2,3,0)

• (0,3,0)

• (2,0,0)

• (0,0,4)

If a linear transformation T: R² →R² is defined as T(x,y) = (4y-5x, x) ,

then find the value of T(1,2).

• (-1,3)

• (3,1)

• (1,3)

• (-3,1)

If a linear Transformation T: V₄ → V₃ is defined as

T(x,y,z,w) = (x +y+z+w, x-y, x+z) , then the value of

T(1,-2,2,4)= ------.

• (3,5,3)

• (3,3,5)

• (5,3,3)

• (5,-3,-3)

A linear Transformation T: V₃ →V₂ is defined as T(x,y,z)=(x-y, x+z).

Find the value of T(u+v) , given that u= (2,2,2) and v= (2,3,4) .

• (10,1)

• (1,10)

• (-1,10)

• (-10,1)

A linear Transformation T: R² → R³ is defined as T(x,y) = (x+y,x-y,y) .

Find the value of T(αu) given that u= (2,4) and α =3 .

• (18,-6,12)

• (-18,6,12)

• (-18,6,-12)

• (18,6,12)