T Show that T(a, b) = (a - b, a + 2b) is a linear transformation....

 

Transcribed Image Text:

T Show that T(a, b) = (a - b, a + 2b) is a linear transformation. (4 Marks) b.) Let T be a linear transformation from V to W. Show that T is injective if and only if the Kernel of T is {0} (3 Marks) c.) Find the matrix of transformation of, (4 Marks) i.) T(a, b) = (a b, 2a - 3b) in the standard basis H.A ii.) T(a, b, c) = (2a - b, a +3c, a 2b = c) - Q.A.A in the standard basis d.) Write the matrix representation of T(a, b) = (a 2b, 2a - 3b) in, (5 Marks) i.) Standard basis ii.) B= {(2, 1), (-1, 2)}. e.) Show that a linear transformation T:VW is one to one mapping if and only if ker(T) = {0}. (4 Marks) T Show that T(a, b) = (a - b, a + 2b) is a linear transformation. (4 Marks) b.) Let T be a linear transformation from V to W. Show that T is injective if and only if the Kernel of T is {0} (3 Marks) c.) Find the matrix of transformation of, (4 Marks) i.) T(a, b) = (a b, 2a - 3b) in the standard basis H.A ii.) T(a, b, c) = (2a - b, a +3c, a 2b = c) - Q.A.A in the standard basis d.) Write the matrix representation of T(a, b) = (a 2b, 2a - 3b) in, (5 Marks) i.) Standard basis ii.) B= {(2, 1), (-1, 2)}. e.) Show that a linear transformation T:VW is one to one mapping if and only if ker(T) = {0}. (4 Marks)