High School Mathematics Extensions/Matrices/Problem Set/Solutions

From Wikibooks, the open-content textbooks collection

< High School Mathematics Extensions | Matrices | Problem Set

Current revision (unreviewed)

Note: The best way to view these pages is to set your Math Preferences to "Always Render PNG".

Content
HSME
Matrices
Recurrence Relations
Problems & Projects
Problem Set
Project
Soultions
Exercises Solutions
Problem Set Solutions
Misc.
Definition Sheet
Full Version

[edit] Matrices Problem Set

At the moment, the main focus is on authoring the main content of each chapter. Therefore this exercise solutions section may be out of date and appear disorganised.

If you have a question please leave a comment in the "discussion section" or contact the author or any of the major contributors.

1.

$\begin{pmatrix} 2&3\\ 3&5\end{pmatrix} \begin{pmatrix} ?&?&?&?\\ ?&?&?&?\end{pmatrix} =\begin{pmatrix} 28&94&70&102\\ 44&153&112&163\end{pmatrix}$

$\begin{pmatrix} 2&3\\ 3&5\end{pmatrix}^{-1} \begin{pmatrix} 2&3\\ 3&5\end{pmatrix} \begin{pmatrix} ?&?&?&?\\ ?&?&?&?\end{pmatrix} =\begin{pmatrix} 2&3\\ 3&5\end{pmatrix}^{-1} \begin{pmatrix} 28&94&70&102\\ 44&153&112&163\end{pmatrix}$

$\begin{pmatrix} ?&?&?&?\\ ?&?&?&?\end{pmatrix} =\begin{pmatrix} 2&3\\ 3&5\end{pmatrix}^{-1} \begin{pmatrix} 28&94&70&102\\ 44&153&112&163\end{pmatrix}$

$=\frac{1}{2 \times 5 - 3 \times 3} \begin{pmatrix} 5&-3\\ -3&2\end{pmatrix} \begin{pmatrix} 28&94&70&102\\ 44&153&112&163\end{pmatrix}$

$=\begin{pmatrix} (5\times28+(-3)\times44)&(5\times94+(-3)\times153)& (5\times70+(-3)\times112)&(5\times102+(-3)\times163)\\ ((-3)\times28+2\times44)&((-3)\times94+2\times153)& ((-3)\times70+2\times112)&((-3)\times102+2\times163)\end{pmatrix}$