031 Review Part 2, Problem 8 - Revision history

Kayla Murray at 20:38, 15 October 2017

2017-10-15T20:38:12Z

Kayla Murray at 03:19, 11 October 2017

2017-10-11T03:19:57Z

Kayla Murray at 02:56, 11 October 2017

2017-10-11T02:56:44Z

Kayla Murray at 02:16, 10 October 2017

2017-10-10T02:16:56Z

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

2017-10-10T01:59:42Z

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:'''

{| 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 6: / Line 6: @@
 & 2 & 5
           \end{bmatrix}.</math>&nbsp; Find &nbsp;<math style="vertical-align: 0px">A^{-1}</math>&nbsp; if possible.
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
@@ Line 81: / Line 80: @@
 & -3 & 2\\
 & 1 & -1
-          \end{array}\right]</math>
+          \end{array}\right].</math>
 |}
@@ Line 94: / Line 93: @@
           \end{array}\right]</math>
 |}
-[[031_Review_Part_2|'''<u>Return to Sample Exam</u>''']]
+[[031_Review_Part_2|'''<u>Return to Review Problems</u>''']]

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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 35: / Line 88: @@
 !Final Answer: &nbsp;
 |-
-|&nbsp;&nbsp; &nbsp; &nbsp;
+|&nbsp;&nbsp; &nbsp; &nbsp; <math>A^{-1}=\left[\begin{array}{ccc}
 |}
 [[031_Review_Part_2|'''<u>Return to Sample Exam</u>''']]

@@ Line 11: / Line 11: @@
 !Foundations: &nbsp;
 |-
+|To find the inverse of a matrix &nbsp;<math style="vertical-align: -4px">A,</math>&nbsp; you augment the matrix &nbsp;<math style="vertical-align: 0px">A</math>&nbsp;
 |}