A First Course in Linear Algebra · Problem B.C12

Vector Spaces — Robert Beezer

Mathematics — Linear Algebra · basis-matrix-space

Problem

Find a basis for the vector space

T

of lower triangular

3 \times 3

matrices; that is, matrices of the form

\begin{bmatrix}* & 0 & 0\\* & * & 0\\* & * & *\end{bmatrix}

where an asterisk represents any complex number.