Difference between revisions of "031 Review Part 2, Problem 9"

Revision as of 18:11, 10 October 2017

If $A$ is an $n\times n$ matrix such that $AA^{T}=I,$ what are the possible values of ${\text{det }}A?$

Foundations:
Recall:
1. ${\text{det }}(AB)=({\text{det }}A)({\text{det }}B)$
2. ${\text{det }}I=n$
3. ${\text{det }}A^{T}={\text{det }}A$

Solution:

Step 1:

Step 2:

Final Answer:

@@ Line 5: / Line 5: @@
 !Foundations: &nbsp;
 |-
-|
+|Recall:
+|-
+|'''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>
+|-
+|'''3.''' &nbsp;<math style="vertical-align: 0px">\text{det }A^T=\text{det }A</math>
 |}