031 Review Part 2, Problem 5 - Revision history

Kayla Murray at 20:29, 15 October 2017

2017-10-15T20:29:59Z

Kayla Murray at 03:48, 12 October 2017

2017-10-12T03:48:05Z

Kayla Murray at 03:43, 12 October 2017

2017-10-12T03:43:10Z

Kayla Murray at 22:35, 11 October 2017

2017-10-11T22:35:13Z

Kayla Murray at 02:09, 10 October 2017

2017-10-10T02:09:56Z

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

2017-10-10T01:56:54Z

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;"
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|   '''(a)'''    
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|   '''(b)'''    
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[[031_Review_Part_2|'''Return to Sample Exam''']]

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 <span class="exam">(b) &nbsp;<math style="vertical-align: -7px">\text{det }(A^TB^{-1})</math>
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
@@ Line 93: / Line 92: @@
 |&nbsp;&nbsp; '''(b)''' &nbsp; &nbsp; <math>\text{det }(A^TB^{-1})=-2</math>
 |}
-[[031_Review_Part_2|'''<u>Return to Sample Exam</u>''']]
+[[031_Review_Part_2|'''<u>Return to Review Problems</u>''']]

@@ 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: 0px">A</math>&nbsp; and &nbsp;<math style="vertical-align: 0px">B</math>&nbsp; be &nbsp;<math style="vertical-align: 0px">6\times 6</math>&nbsp; matrices with &nbsp;<math style="vertical-align: -1px">\text{det }A=-10</math>&nbsp; and &nbsp;<math style="vertical-align: 0px">\text{det }B=5.</math>&nbsp; Use properties of determinants to compute:
-::<math>B=
+<span class="exam">(a) &nbsp;<math style="vertical-align: -2px">\text{det }3A</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) &nbsp;<math style="vertical-align: -7px">\text{det }(A^TB^{-1})</math>

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 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 !Step 1: &nbsp;
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 |}
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 !Step 2: &nbsp;
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@@ Line 73: / Line 89: @@
 !Final Answer: &nbsp;
 |-
-|&nbsp;&nbsp; '''(a)''' &nbsp; &nbsp; <math>\text{det }(3A)=-7290.</math>
+|&nbsp;&nbsp; '''(a)''' &nbsp; &nbsp; <math>\text{det }(3A)=-7290</math>
 |-
-|&nbsp;&nbsp; '''(b)''' &nbsp; &nbsp;
+|&nbsp;&nbsp; '''(b)''' &nbsp; &nbsp; <math>\text{det }(A^TB^{-1})=-2</math>
 |}
 [[031_Review_Part_2|'''<u>Return to Sample Exam</u>''']]

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