Let U be a square matrix such that U'U=I. Show that det U = +1. Assume that U'U=1, Since the desired result is that det U= +1, an intermediate step must be found which contains the expression det U. Which of the following can be applied to the assumption U'U=I to achieve the desired result? O A. det (U'u)-1 = det I O B. det (UU)=1 OC. det (U'u) = det I O D. (U'U)-1=11 Simplify the right side of the equation found in the first step.
Let U be a square matrix such that U'U=I. Show that det U = +1. Assume that U'U=1, Since the desired result is that det U= +1, an intermediate step must be found which contains the expression det U. Which of the following can be applied to the assumption U'U=I to achieve the desired result? O A. det (U'u)-1 = det I O B. det (UU)=1 OC. det (U'u) = det I O D. (U'U)-1=11 Simplify the right side of the equation found in the first step.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Let U be a square matrix such that u'U=I. Show that det U = +1.
Assume that u'u=1, Since the desired result is that det U= +1, an intermediate step must be found which contains the expression det U. Which of the following can be applied to the assumption U'U=I to achieve the desired result?
O A. det (U'u)-1= det I
O B. det (Uu) = I
OC. det (U'u) = det I
OD. (UTu)-1=1-1
Simplify the right side of the equation found in the first step.
Which property can be used
simplify the left side of the equation found in the first step? Select all that apply.
O A. det U = - det U
O B. UTU=1
O C. Multiplicative Property
O D. Commutative Property
O E. det U = det U
Use the properties from the previous step to rewrite the left side of the equation found in the first step.
Setting each side of the equation in the first step equal to the expressions found in previous steps and solving for det U results in det U=1.
Click to select your answer(s).
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