Let U be a square matrix such that Upper U Superscript Upper TUequalsI. Show that det Uequalsplus or minus1. Assume that Upper U
Superscript Upper TUequalsI. Since the desired result is that det Uequalsplus or minus1, an intermediate step must be found which contains the expression det U. Which of the following can be applied to the assumption Upper U Superscript Upper TUequalsI to achieve the desired result? A. det (Upper U Superscript Upper TU)Superscript negative 1equalsdet I B. det (Upper U Superscript Upper TU)equalsI C. (Upper U Superscript Upper TU)Superscript negative 1equalsISuperscript negative 1 D. det (Upper U Superscript Upper TU)equalsdet I Simplify the right side of the equation found in the first step. nothing Which property can be used to simplify the left side of the equation found in the first step? Select all that apply.
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Answer:
Step-by-step explanation:
Given
Required
The measure of each angle
First, we calculate the length of the three sides of the triangle.
This is calculated using distance formula
For AB
So:
For BC
For AC
So, we have:
By representation
So, we have:
By cosine laws, the angles are calculated using:
Collect like terms
Solve for
Take arc cos of both sides
Collect like terms
Solve for
Take arc cos of both sides
For the third angle, we use:
--- angles in a triangle
Make C the subject