Exercise 3.1.23

Answers

The extra column $b$ enlarges the column space unless $b$ is already in the column space.

[\begin{matrix} A & b \end{matrix}] = [\begin{matrix} 1 & 0 & 1 \\ 0 & 0 & 1 \end{matrix}] \begin{aligned} (larger column space) \\ (no solution to Ax = b) \end{aligned} [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 1 \end{matrix}] \begin{aligned} (b is in column space) \\ (Ax = b has a solution) \end{aligned}

mathchakra

2022-01-16 13:25