Definitions

If T:V→W is a lineaer transformation such that the rank is 3 and dimension of V is 4, then find the nullity.

• 1

• 2

• 3

• 4

If T:V→W is a lineaer transformation such that rank is 3 and nullity is 1, then dim(V)=---

• 4

• 3

• 2

• 1

If T:V→W is a lineaer transformation such that the nullity is 3 and dimension of V is 4, then find the rank.

• 1

• 2

• 3

• 4

A linear transformation T is defined as T(x,y)=(2x,2y) then, T(e₁)=

• (2,0)

• (0,0)

• (0,1)

• (1,1)

If determinant value of a (3xX) matrix is zero then the vectors are -------

• linearly dependent

• linearly independent

• perpendicular

• symmetric

If determinant value of a (3xX) matrix is not zero then the vectors are -------

• linearly dependent

• linearly independent

• perpendicular

• symmetric

A linear transformation T is defined as T(x,y)=(2x,2y) then, T(e₂)=

• (0,2)

• (2,0)

• (0,0)

• (1,1)

A linear transformation T is defined as T(v)= T(x,y,z)=(2x,2y,3z) then, T(1,2,3)=

• (2,4,9)

• (1,2,3)

• (1,1,1)

• (1,1,0)

A linear transformation T is defined as T(v)=2v, find T(2,3)

• (4,6)

• (1,1)

• (2,3)

• (4,3)

A linear transformation T is defined as T(v)=2v then, findT(x+y) for x=[1,1] and y=[0,1]

• [2,4]

• [1,2]

• [1,1]

• [0,1]