A First Course in Linear Algebra · Problem RQ-PD.3

Determinants — Robert Beezer

Mathematics — Linear Algebra · dimension-four-subspaces

Problem

Row-reduce the matrix

A

to reduced row-echelon form. Without any further computations, compute the dimensions of the four subspaces, (a)

\mathcal{N}(A)

, (b)

\mathcal{C}(A)

, (c)

\mathcal{R}(A)

and (d)

\mathcal{L}(A)

A = \begin{bmatrix} 1 & -1 & 2 & 8 & 5 \\ 1 & 1 & 1 & 4 & -1 \\ 0 & 2 & -3 & -8 & -6 \\ 2 & 0 & 1 & 8 & 4 \end{bmatrix}