Determinefthe set isa basis for R Jstity your anwer he gven setabass for R OA. Yes, becaune these tvee vectors form the columna of an inveribie 33 matrik. By the invertble mati theorem, he follouing statements are equivalent A s an invertble matix, the columna of A fom a linearly independent set and the columns of A span R OB. No. because these thvee vectors form the cokumns of an invertble 33 matix By the invertble mati theorem, the folloving statements are equivalent A is a singular matrik, the columns of A fom a lineary independent et and he columns of Aspan O. Yes. because hese thvee vectors form the columns of a matk that is not invertible By the inverible mati theorem, the following statements are equvalent A isa singular matrik the columns of A forma lineaty indepandent set and the columns of A span R OD. No. becaune these tre vectero form the cokums of a3 matte that is not inverikie By the inverikie mati theorem, the folowing statemerts are eguhalent A is an inverikie matie. the columns of A form a lnoarty

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Topic Video
Question

Need help please.

Determine if the set is a basis for R. Justify your answer.
ls the given set a basis for R?
OA. Yes, because these three vectors form the columns of an invertble 3x3 matrik. By the invertible matix theorem, the follouing statements are equivalent A is an invertble mati, the columns of A form a linearly
independent set, and the columns of A span R".
OB. No. because these three vectors form the columns of an invertible 3x3 mati. By the inverible matrix theorem, the following statements are equivalent A is a singular matrik, the columns of A fom a linearly independent
set and the columns of A span R".
OC. Yes. because these three vectors form the columns of a 3x3 matrix that is not invertible. By the invertible matrix theorem, the following statements are equivalent A is a singular matrix, the columns of A form a lineaty
independent set and the columns of A span R.
OD. No. because these tree vectors form the columns of a 3x3 matix that is not inverible. By the inverible matrix theorem, the following statements are equlvalent A is an inveribie matrix, the columns of A form a ineary
Independent set and the columns of A span R".
Transcribed Image Text:Determine if the set is a basis for R. Justify your answer. ls the given set a basis for R? OA. Yes, because these three vectors form the columns of an invertble 3x3 matrik. By the invertible matix theorem, the follouing statements are equivalent A is an invertble mati, the columns of A form a linearly independent set, and the columns of A span R". OB. No. because these three vectors form the columns of an invertible 3x3 mati. By the inverible matrix theorem, the following statements are equivalent A is a singular matrik, the columns of A fom a linearly independent set and the columns of A span R". OC. Yes. because these three vectors form the columns of a 3x3 matrix that is not invertible. By the invertible matrix theorem, the following statements are equivalent A is a singular matrix, the columns of A form a lineaty independent set and the columns of A span R. OD. No. because these tree vectors form the columns of a 3x3 matix that is not inverible. By the inverible matrix theorem, the following statements are equlvalent A is an inveribie matrix, the columns of A form a ineary Independent set and the columns of A span R".
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Research Design Formulation
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning