Matrix Theory (MAS 2103)
Homework 1 (due Friday, 8/30/2024 by 11:59pm)
Name: Abigail Clermont
Last Four digits of Z-number: 7361
Scan your work into a single PDF file and then upload it to Homework 1 on Canvas.
1. Consider the three systems of linear equations whose augmented matrices are given below:
$\begin{pmatrix} 1 & 0 & 8 & -5 & 6 \ 0 & 1 & 4 & -9 & 3 \ 0 & 0 & 1 & 1 & 2 \end{pmatrix}$ (a) $\begin{pmatrix} 1 & -3 & 4 & 7 \ 0 & 1 & 2 & 2 \ 0 & 0 & 1 & 5 \end{pmatrix}$ (b) $\begin{pmatrix} 1 & -3 & 7 & 1 \ 0 & 1 & 4 & 0 \ 0 & 0 & 0 & 1 \end{pmatrix}$ (c)
Which system has no solution, which has exactly one solution, and which has infinitely many solutions?
Show work to justify your answers.
2. Consider the foll