Linear Algebra and Its Applications · Problem 2.4.24

Vector Spaces — Gilbert Strang

Mathematics · four-fundamental-subspaces

Problem

What are the dimensions of the four subspaces for

A

B

, and

C

, if

I

is the 3 by 3 identity matrix and

0

is the 3 by 2 zero matrix?

A = \begin{bmatrix} I & 0 \end{bmatrix} \quad \text{and} \quad B = \begin{bmatrix} I & I \\ 0^T & 0^T \end{bmatrix} \quad \text{and} \quad C = \begin{bmatrix} 0 \end{bmatrix}.