I will ask you to find the eigenvalues and bases of the corresponding
eigenspaces for a simple matrix. Here are some examples you can use
for practice.

<p> 

<b>Example 1</b><br> Suppose A is this 2x2 matrix:
<pre><font size=+1> [1 2]
 [0 3].</font></pre>
Find the eigenvalues and bases for each eigenspace.

<br>
<a href="q8a1.html">An answer is here.</a>

<p>

<b>Example 2</b><br> Suppose A is this 2x2 matrix:
<pre><font size=+1> [2 3]
 [1 4].</font></pre>
Find the eigenvalues and bases for each eigenspace.

<br>
<a href="q8a2.html">An answer is here.</a>

<p>

<b>Example 3</b><br> Suppose A is this 3x3 matrix:
<pre><font size=+1> [1 &nbsp;1 0]
 [0 &nbsp;2 0]
 [0 &ndash;1 4].</font></pre>
Find the eigenvalues and bases for each eigenspace.

<br>
<a href="q8a3.html">An answer is here.</a>

<p>

<b>Example 4</b><br> Suppose A is this 3x3 matrix:
<pre><font size=+1> [1 &nbsp;1 0]
 [0 &nbsp;2 0]
 [0 &ndash;1 2].</font></pre>
Find the eigenvalues and bases for each eigenspace.

<br>
<a href="q8a4.html">An answer is here.</a>

<p>

<b>Example 5</b><br> Suppose A is this 3x3 matrix:
<pre><font size=+1> [&nbsp;0 0 2]
 [&ndash;3 1 6]
 [&nbsp;0 0 1].</font></pre>
Find the eigenvalues and bases for each eigenspace.

<br>
<a href="q8a5.html">An answer is here.</a>