031 Review Part 3, Problem 7 - Revision history

Kayla Murray at 21:03, 15 October 2017

2017-10-15T21:03:37Z

Kayla Murray at 17:34, 13 October 2017

2017-10-13T17:34:23Z

Kayla Murray at 17:25, 13 October 2017

2017-10-13T17:25:21Z

Kayla Murray at 17:21, 13 October 2017

2017-10-13T17:21:59Z

Kayla Murray at 02:28, 10 October 2017

2017-10-10T02:28:33Z

Kayla Murray: Created page with "Consider the matrix $A= \begin{bmatrix} 1 & -4 & 9 & -7 \\ -1 & 2 & -4 & 1 \\..."$

2017-10-10T02:04:02Z

Created page with "Consider the matrix <math style="vertical-align: -31px">A= \begin{bmatrix} 1 & -4 & 9 & -7 \\ -1 & 2 & -4 & 1 \\..."

New page

Consider the matrix  <math style="vertical-align: -31px">A=
\begin{bmatrix}
1 & -4 & 9 & -7 \\
-1 & 2 & -4 & 1 \\
5 & -6 & 10 & 7
\end{bmatrix}</math>  and assume that it is row equivalent to the matrix

::<math>B=
\begin{bmatrix}
1 & 0 & -1 & 5 \\
0 & -2 & 5 & -6 \\
0 & 0 & 0 & 0
\end{bmatrix}.</math>

(a) List rank  <math style="vertical-align: 0px">A</math>  and  <math style="vertical-align: 0px">\text{dim Nul }A.</math>

(b) Find bases for  <math style="vertical-align: 0px">\text{Col }A</math>  and  <math style="vertical-align: 0px">\text{Nul }A.</math>  Find an example of a nonzero vector that belongs to  <math style="vertical-align: -5px">\text{Col }A,</math>  as well as an example of a nonzero vector that belongs to  <math style="vertical-align: 0px">\text{Nul }A.</math>

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
!Foundations:  
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'''Solution:'''

'''(a)'''

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{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
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'''(b)'''

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{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
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{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
!Final Answer:  
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|   '''(a)'''    
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|   '''(b)'''    
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[[031_Review_Part_3|'''Return to Sample Exam''']]

@@ Line 14: / Line 14: @@
 <span class="exam">Use the Diagonalization Theorem to find the eigenvalues of &nbsp;<math style="vertical-align: 0px">A</math>&nbsp; and a basis for each eigenspace.
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
@@ Line 106: / Line 105: @@
           \end{bmatrix}\Bigg\}.</math>
 |}
-[[031_Review_Part_3|'''<u>Return to Sample Exam</u>''']]
+[[031_Review_Part_3|'''<u>Return to Review Problems</u>''']]

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 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 !Step 2: &nbsp;
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+|
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 !Final Answer: &nbsp;
 |-
-|&nbsp;&nbsp; &nbsp; &nbsp;
+|&nbsp; &nbsp; &nbsp; &nbsp; The eigenvalues of &nbsp;<math style="vertical-align: 0px">A</math>&nbsp; are &nbsp;<math style="vertical-align: 0px">3</math>&nbsp; and &nbsp;<math style="vertical-align: -1px">4.</math>&nbsp;
 |}
 [[031_Review_Part_3|'''<u>Return to Sample Exam</u>''']]

@@ Line 1: / Line 1: @@
-<span class="exam">Consider the matrix &nbsp;<math style="vertical-align: -31px">A=
+<span class="exam">Let &nbsp;<math>A=\begin{bmatrix}
-    \begin{bmatrix}
+& 0 & -1 \\
-& -4 & 9 & -7 \\
+& 1 &-3\\
-            -1 & 2  & -4 & 1 \\
+& 0 & 0
-& -6 & 10 & 7
+         \end{bmatrix}\begin{bmatrix}
-          \end{bmatrix}</math>&nbsp; and assume that it is row equivalent to the matrix
+& 0 & 0 \\
-::<math>B=
+<span class="exam">Use the Diagonalization Theorem to find the eigenvalues of &nbsp;<math style="vertical-align: 0px">A</math>&nbsp; and a basis for each eigenspace.
@@ Line 26: / Line 24: @@
 '''Solution:'''
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
@@ Line 59: / Line 41: @@
 !Final Answer: &nbsp;
 |-
-|&nbsp;&nbsp; '''(a)''' &nbsp; &nbsp;
+|&nbsp;&nbsp; &nbsp; &nbsp;
 |}
 [[031_Review_Part_3|'''<u>Return to Sample Exam</u>''']]

@@ Line 35: / Line 35: @@
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 !Step 1: &nbsp;
 |-
+|
 |}

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 !Foundations: &nbsp;
 |-
+|'''Diagonalization Theorem'''
 |}