031 Review Part 1, Problem 5 - Revision history

Kayla Murray at 19:18, 15 October 2017

2017-10-15T19:18:54Z

2017-10-09T20:49:16Z

2017-10-09T20:15:51Z

@@ Line 34: / Line 34: @@
 |Hence, this statement is false.
 |}
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
@@ Line 40: / Line 41: @@
 |&nbsp;&nbsp; &nbsp; &nbsp; FALSE
 |}
-[[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.
+|Let &nbsp;<math style="vertical-align: -20px">A=
 |-
-|So, we have
+|Notice that
 |-
+|
-&nbsp; &nbsp; &nbsp; &nbsp;<math>\begin{array}{rcl}
+::<math>\text{det} A=\text{det} B=1.</math>
-\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}}\\
+|-
-&&\\
+|Since &nbsp;<math style="vertical-align: -6px">\text{det} A,\text{det} B\neq 0,</math>&nbsp; we know &nbsp;<math style="vertical-align: 0px">A</math>&nbsp; and &nbsp;<math style="vertical-align: 0px">B</math>&nbsp; are invertible.
-& \overset{L'H}{=} & \displaystyle{\frac{-4}{10}}\\
+|-
-&&\\
+|But,
-& = & \displaystyle{-\frac{2}{5}}.
+|-
-\end{array}</math>
 |}
@@ Line 21: / Line 38: @@
 !Final Answer: &nbsp;
 |-
-|&nbsp;&nbsp; &nbsp; &nbsp; False
+|&nbsp;&nbsp; &nbsp; &nbsp; FALSE
 |}
 [[031_Review_Part_1|'''<u>Return to Sample Exam</u>''']]

← Older revision		Revision as of 20:15, 9 October 2017
Line 1:		Line 1:
−	<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>  and  <math style="vertical-align: 0px">B</math>  are invertible  <math style="vertical-align: 0px">n\times n</math>  matrices, then so is  <math style="vertical-align: -1px">A+B.</math>

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