# Matrix Representation of Linear Transformations

• October 4th 2008, 08:30 PM
Qt3e_M3
Matrix Representation of Linear Transformations
Let V be an n-dimensional vector space with an ordered basis B.
Define T: V F^n by T(x) = [x]B. Prove that T is linear.

Note that the [x]B is suppose to be a subscript B
• October 4th 2008, 08:55 PM
ThePerfectHacker
Quote:

Originally Posted by Qt3e_M3
Let V be an n-dimensional vector space with an ordered basis B.
Define T: V F^n by T(x) = [x]B. Prove that T is linear.

Note that the [x]B is suppose to be a subscript B

You just need to show: (i) $T(k\bold{v}) = kT(\bold{v})$ i.e. $[k\bold{v}]_B = k[\bold{v}]_B$ (ii) $T(\bold{v}+\bold{w}) = T(\bold{v}) + T(\bold{w})$ i.e. $[\bold{v}+\bold{w}]_B = [\bold{v}]_B + [\bold{w}]_B$.