Rank and Nullity of linear transformations and matrices
Let T:R3→R2 be the linear transformation defined by T(x, y, z) = (x, z), where x, y, z ∈ R. Let A = {(x, y, z) ∈ R3 : T(x, y, z) = (0, 0)} and B = {T(x, y, z): (x, y, z) ∈ R3}.Then
Let T:R2→R2 be the linear transformation defined by T(x, y) = (x, 0), where x, y ∈ R. Then B={(x, y) ∈ R2 : T(x, y)=(x, y)} equals
Let T:R2→R be the linear transformation defined by T(x, y) = x, where x, y ∈ R . Then A = {(x, y) ∈ R 2 : T(x, y) = 0} equals
Let T:R2→R2 be the linear transformation defined by T(x, y) = (x, x+y), where x, y ∈ R. Let A = {(x, y) ∈ R2 : T(x, y) = (0, 0)}and B = {(x, y) ∈ R2 : T(x, y) = (1, 0)}. Then
Let T:R2→R4 be the linear transformation defined by T(x, y) = (x, x+y, 0, 0), where x, y ∈ R. Then order of matrix representation of the linear transformation T is