Rank and nullity of linear transformations and matrices
Let 3→2 be the linear transformation defined by , where ∈ . Let = {() ∈ 3 : = (0, 0)} and = { ∈ 3}.Then
Let 2→2 be the linear transformation defined by , where ∈ . Then { ∈ 2 : } equals
Let 2→ be the linear transformation defined by , where ∈ . Then = { ∈ 2 : = 0} equals
Let 2→2 be the linear transformation defined by , where ∈ . Let = { ∈ 2 : }and = { ∈ 2 : }. Then
Let 2→4 be the linear transformation defined by , where ∈ . Then order of matrix representation of the linear transformation is