Exercise 3.3.24

Answers

(a): $[\begin{matrix} 1 \\ 1 \end{matrix}] [x] = [\begin{matrix} b_{1} \\ b_{2} \end{matrix}]$ has 0 or 1 solutions, depending on $b$
(b): $[\begin{matrix} 1 & 1 \end{matrix}] [\begin{matrix} x_{1} \\ x_{2} \end{matrix}] =$ $[b]$ has infinitely many solutions for every $b$
(c): There are 0 or $\infty$ solutions when $A$ has rank $r < m$ and $r < n$ : the simplest example is a zero matrix.
(d): one solution for all $b$ when $A$ is square and invertible (like $A = I$ ).

mathchakra

2022-01-23 15:07