031 Review Part 1, Problem 6 - Revision history

Kayla Murray at 19:19, 15 October 2017

2017-10-15T19:19:30Z

2017-10-09T21:01:42Z

2017-10-09T20:16:23Z

@@ Line 25: / Line 25: @@
 |So, the statement is true.
 |}
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
@@ Line 31: / Line 32: @@
 |&nbsp;&nbsp; &nbsp; &nbsp; TRUE
 |}
-[[031_Review_Part_1|'''<u>Return to Sample Exam</u>''']]
+[[031_Review_Part_1|'''<u>Return to Review Problems</u>''']]

@@ Line 4: / Line 4: @@
 !Solution: &nbsp;
 |-
-|First, we switch to the limit to <math style="vertical-align: 0px">x</math> so that we can use L'Hopital's rule.
+|By the Rank Theorem, we have
 |-
+|
 &nbsp; &nbsp; &nbsp; &nbsp;<math>\begin{array}{rcl}
-\displaystyle{\lim_{x \rightarrow \infty}\frac{3-2x^2}{5x^2 + x +1}} & \overset{L'H}{=} & \displaystyle{\lim_{x \rightarrow \infty}\frac{-4x}{10x+1}}\\
+\displaystyle{5} & = & \displaystyle{\text{dim Col }A+\text{dim Nul }A}\\
 &&\\
-& = & \displaystyle{-\frac{2}{5}}.
+& = & \displaystyle{\text{dim Col }A+2.}
 \end{array}</math>
 |}
@@ Line 21: / Line 29: @@
 !Final Answer: &nbsp;
 |-
-|&nbsp;&nbsp; &nbsp; &nbsp; False
+|&nbsp;&nbsp; &nbsp; &nbsp; TRUE
 |}
 [[031_Review_Part_1|'''<u>Return to Sample Exam</u>''']]

← Older revision		Revision as of 20:16, 9 October 2017
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−	<span class="exam">True or false: If ~~all the entries of~~ a  <math style="vertical-align: 0px">7\times 7</math>  matrix  <math style="vertical-align: ~~0px~~">A</math>  ~~are~~  <math style="vertical-align: ~~-4px~~">7,</math>  ~~then~~  <math style="vertical-align: 0px">\~~text~~{~~det~~ }A</math>  ~~must be~~  <math style="vertical-align: 0px">7^7.</math>	+	<span class="exam"> True or false: If  <math style="vertical-align: 0px">A</math>  is a  <math style="vertical-align: 0px">3\times 5</math>  matrix and  <math style="vertical-align: -4px">\text{dim Nul }A=2,</math>  then  <math style="vertical-align: 0px">A\vec{x}=\vec{b}</math>  is consistent for all  <math style="vertical-align: 0px">\vec{b}</math>  in  <math style="vertical-align: 0px">\mathbb{R}^3.</math>

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