Linear Algebra and Its Applications · Problem 2.5.10

Vector Spaces — Gilbert Strang

Mathematics · graphs-and-networks

Problem

Draw a graph with numbered and directed edges (and numbered nodes) whose incidence matrix is A=[−1100−1010010−100−11].A = \begin{bmatrix} -1 & 1 & 0 & 0 \\ -1 & 0 & 1 & 0 \\ 0 & 1 & 0 & -1 \\ 0 & 0 & -1 & 1 \end{bmatrix}. Is this graph a tree? (Are the rows of AA independent?) Show that removing the last edge produces a spanning tree. Then the remaining rows are a basis for \_\_\_\_?

Browse the problem library