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 IO B. det (Uu) = IOC. det (U'u) = det IO D. (UTu)-1=1-1Simplify the right side of the equation found in the first step.Which property can be usedsimplify the left side of the equation found in the first step? Select all that apply.O A. det U = - det UO B. UTU=1O C. Multiplicative PropertyO D. Commutative PropertyO E. det U = det UUse 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).

Answered: Image /qna-images/answer/cd964473-019b-4f55-9e5b-49526dacb34b.jpg

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 resulr? OA. det (U'u)-1= det I OB. det (UTu) =1 OC. det (UTu)=det 1 O D. (UTU)-1=1-1 Simplify the right side of the equation found in the first step. Which property can be used to simplify the left side of the equation found in the first step? Select all that apply. OA. det U = - det U OB. UTU=1 OC. Multiplicative Property O D. Commutative Property DE. det U= det U Use the properties from the previous step to rewrite the left side of the equation found in the first step. (2 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).

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 resulr? OA. det (U'u)-1= det I OB. det (UTu) =1 OC. det (UTu)=det 1 O D. (UTU)-1=1-1 Simplify the right side of the equation found in the first step. Which property can be used to simplify the left side of the equation found in the first step? Select all that apply. OA. det U = - det U OB. UTU=1 OC. Multiplicative Property O D. Commutative Property DE. det U= det U Use the properties from the previous step to rewrite the left side of the equation found in the first step. (2 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).

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.

Question

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
O D. (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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