# MTH212 Solutions

MTH212 Tma Solutions

1. Linear transformations are also called vector space __________________

Isomorphism

Inverse

—>> homomorphisms.

Dimension

2. The rank of T is defined to be the _______________________of R(T), the range space of T.

projection

Kernel

function

—>> dimension

3. There are two sets which are associated with any linear transformation, T. These are the range and the ___________________of T

Projection

—>> Kernel

Function

Inverse

4. If T is an isomorphism between U and V then \(T^{-1}\) is an isomorphism between________________________

—>> \(V and U\)

\(U and T^{-1}\)

\(V^{-1} and U\)

\(V and T^{-1}\)

5. Let T:Uâ†’V be a linear transformation; If T is injective, we also say T is ______________________

Onto

Surjective

one-zero

—>> one-one

6. The __________________operator is both one-one and onto

Inverse

—>> Identity

Dimension

Range

7. Let U and V be vector spaces over a field F, and let \(T:U \rightarrow V\) be a one-one and onto linear transformation. The T is called an