Exercise 3.3.13

Answers

(a): The particular solution $x_{p}$ is always multiplied by $1$ ;
(b): Any solution can be $x_{p}$ ;
(c): $[\begin{matrix} 3 & 3 \\ 3 & 3 \end{matrix}] [\begin{matrix} x \\ y \end{matrix}] = [\begin{matrix} 6 \\ 6 \end{matrix}]$ . Then $[\begin{matrix} 1 \\ 1 \end{matrix}]$ is shorter (length $\sqrt{2}$ ) than $[\begin{matrix} 2 \\ 0 \end{matrix}]$ (length 2)
(d): The only "homogeneous" solution in the nullspace is $x_{n} = 0$ when $A$ is invertible.

mathchakra

2022-01-23 15:00