031 Review Part 2, Problem 9 - Revision history

Kayla Murray at 20:40, 15 October 2017

2017-10-15T20:40:40Z

Kayla Murray at 02:30, 11 October 2017

2017-10-11T02:30:01Z

Kayla Murray at 01:11, 11 October 2017

2017-10-11T01:11:58Z

Kayla Murray at 02:17, 10 October 2017

2017-10-10T02:17:26Z

Kayla Murray at 02:00, 10 October 2017

2017-10-10T02:00:36Z

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

2017-10-10T02:00:19Z

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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{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
!Final Answer:  
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[[031_Review_Part_2|'''Return to Sample Exam''']]

@@ Line 1: / Line 1: @@
 <span class="exam">If &nbsp;<math style="vertical-align: 0px">A</math>&nbsp; is an &nbsp;<math style="vertical-align: 0px">n\times n</math>&nbsp; matrix such that &nbsp;<math style="vertical-align: -4px">AA^T=I,</math>&nbsp; what are the possible values of &nbsp;<math style="vertical-align: 0px">\text{det }A?</math>
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
@@ Line 9: / Line 8: @@
 |'''1.''' &nbsp;<math style="vertical-align: -5px">\text{det }(AB)=(\text{det }A)(\text{det }B)</math>
 |-
-|'''2.''' &nbsp;<math style="vertical-align: 0px">\text{det }I=n</math>
+|'''2.''' &nbsp;<math style="vertical-align: 0px">\text{det }I=1</math>
 |-
 |'''3.''' &nbsp;<math style="vertical-align: 0px">\text{det }A^T=\text{det }A</math>
@@ Line 53: / Line 52: @@
 |&nbsp;&nbsp; &nbsp; &nbsp; <math>\text{det }A=\pm 1</math>
 |}
-[[031_Review_Part_2|'''<u>Return to Sample Exam</u>''']]
+[[031_Review_Part_2|'''<u>Return to Review Problems</u>''']]

← Older revision		Revision as of 02:17, 10 October 2017
Line 1:		Line 1:
−	<span class="exam">~~Consider the matrix~~  <math style="vertical-align: ~~-31px~~">A=	+	<span class="exam">If  <math style="vertical-align: 0px">A</math>  is an  <math style="vertical-align: 0px">n\times n</math>  matrix such that  <math style="vertical-align: -4px">AA^T=I,</math>  what are the possible values of  <math style="vertical-align: 0px">\text{det }A?</math>
−	~~\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>~~
−
−	~~<span class="exam">(a) List rank  <math style="vertical-align: 0px">A</math>  and~~  <math style="vertical-align: 0px">\~~text{dim Nul }A.~~</math>
−
−	~~<span class="exam">(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>

← Older revision		Revision as of 02:00, 10 October 2017
Line 26:		Line 26:

	'''Solution:'''		'''Solution:'''
−
−	~~'''(a)'''~~

	{\| class="mw-collapsible mw-collapsed" style = "text-align:left;"		{\| class="mw-collapsible mw-collapsed" style = "text-align:left;"

@@ Line 5: / Line 5: @@
 !Foundations: &nbsp;
 |-
+|Recall:
 |}