• V, W are finite dimentional vector spaces
• T:V→W is a linear transformation

Given:

• Linear map equation T(x)=b, where b ∈ W

To Discuss:

• Existence
• Uniqueness

Discussion:

Existence (Consistency):

 Equation T(x) = b is consistent iff b ∈ Range T

Uniqueness:

 Solution of T(x)=b is unique iff T is one-to-one, if solution exists