031 Review Part 3, Problem 8 - Revision history

Kayla Murray at 21:06, 15 October 2017

2017-10-15T21:06:52Z

Kayla Murray at 03:30, 11 October 2017

2017-10-11T03:30:05Z

Kayla Murray at 02:30, 10 October 2017

2017-10-10T02:30:17Z

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

2017-10-10T02:04:15Z

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)'''

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
!Step 1:  
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{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
!Step 2:  
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'''(b)'''

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
!Step 1:  
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{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
!Step 2:  
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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)'''    
|}
[[031_Review_Part_3|'''Return to Sample Exam''']]

@@ Line 1: / Line 1: @@
 <span class="exam">Give an example of a &nbsp;<math style="vertical-align: 0px">3\times 3</math>&nbsp; matrix &nbsp;<math style="vertical-align: 0px">A</math>&nbsp; with eigenvalues 5,-1 and 3.
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
@@ Line 38: / Line 37: @@
           \end{array}\right].</math>
 |}
-[[031_Review_Part_3|'''<u>Return to Sample Exam</u>''']]
+[[031_Review_Part_3|'''<u>Return to Review Problems</u>''']]

@@ Line 5: / Line 5: @@
 !Foundations: &nbsp;
 |-
+|The eigenvalues of a diagonal matrix are the entries on the diagonal.
 |}
@@ Line 12: / Line 12: @@
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-!Step 1: &nbsp;
+! &nbsp;
 |-
+|
-|}
+::<math>A=\left[\begin{array}{ccc}
+& 0 & 0\\
-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
+& -1 & 0\\
-!Step 2: &nbsp;
+& 0 & 3
 |-
+|Hence, the eigenvalues of &nbsp;<math style="vertical-align: 0px">A</math>&nbsp; are &nbsp;<math style="vertical-align: -4px">5,-1,3.</math>
 |}
@@ Line 27: / Line 32: @@
 !Final Answer: &nbsp;
 |-
-|&nbsp;&nbsp; &nbsp; &nbsp;
+|&nbsp;&nbsp; &nbsp; &nbsp; One example is &nbsp;<math style="vertical-align: -31px">A=\left[\begin{array}{ccc}
 |}
 [[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">Give an example of a &nbsp;<math style="vertical-align: 0px">3\times 3</math>&nbsp; matrix &nbsp;<math style="vertical-align: 0px">A</math>&nbsp; with eigenvalues 5,-1 and 3.
@@ Line 26: / Line 10: @@
 '''Solution:'''
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
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 !Final Answer: &nbsp;
 |-
-|&nbsp;&nbsp; '''(a)''' &nbsp; &nbsp;
+|&nbsp;&nbsp; &nbsp; &nbsp;
 |}
 [[031_Review_Part_3|'''<u>Return to Sample Exam</u>''']]

031 Review Part 3, Problem 8 - Revision history

Kayla Murray at 21:06, 15 October 2017

Kayla Murray at 03:30, 11 October 2017

Kayla Murray at 02:30, 10 October 2017

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

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