Difference between revisions of "031 Review Part 3, Problem 3"

Revision as of 19:23, 9 October 2017

Let $A={\begin{bmatrix}5&1\\0&5\end{bmatrix}}.$

(a) Find a basis for the eigenspace(s) of $A.$

(b) Is the matrix $A$ diagonalizable? Explain.

Foundations:

Solution:

(a)

Step 1:

Step 2:

(b)

Step 1:

Step 2:

Final Answer:
(a)
(b)

@@ Line 1: / Line 1: @@
-<span class="exam">Consider the matrix &nbsp;<math style="vertical-align: -31px">A=
+<span class="exam">Let &nbsp;<math style="vertical-align: -20px">A=
      \begin{bmatrix}
-& -4 & 9 & -7 \\
+& 1 \\
-            -1 & 2  & -4 & 1 \\
+& 5
-& -6 & 10 & 7
+          \end{bmatrix}.</math>
-          \end{bmatrix}</math>&nbsp; and assume that it is row equivalent to the matrix
-::<math>B=
+<span class="exam">(a) Find a basis for the eigenspace(s) of &nbsp;<math style="vertical-align: 0px">A.</math>
-    \begin{bmatrix}
-& 0 & -1 & 5 \\
-& -2  & 5 & -6 \\
-& 0 & 0 & 0
-         \end{bmatrix}.</math>
-<span class="exam">(a) List rank &nbsp;<math style="vertical-align: 0px">A</math>&nbsp; and &nbsp;<math style="vertical-align: 0px">\text{dim Nul }A.</math>
-<span class="exam">(b) Find bases for &nbsp;<math style="vertical-align: 0px">\text{Col }A</math>&nbsp; and &nbsp;<math style="vertical-align: 0px">\text{Nul }A.</math>&nbsp; Find an example of a nonzero vector that belongs to &nbsp;<math style="vertical-align: -5px">\text{Col }A,</math>&nbsp; as well as an example of a nonzero vector that belongs to &nbsp;<math style="vertical-align: 0px">\text{Nul }A.</math>
+<span class="exam">(b) Is the matrix &nbsp;<math style="vertical-align: 0px">A</math>&nbsp; diagonalizable? Explain.