7. Provide a justification for your response to the following questions. a. Suppose that we have vectors in R°, Can every vector b in R° be written as a linear combination of V1, V2,• ••, whose span is R°. V10, V1, V2, ..., V10? b. Suppose that we have vectors in R°, v1, V2, ..., V10, whose span is R°. Can every vector b in R° be written uniquely as a linear combination of V1, V2,· ••, V10? С. Do the vectors ei = e2 = ez = cnan m3,
7. Provide a justification for your response to the following questions. a. Suppose that we have vectors in R°, Can every vector b in R° be written as a linear combination of V1, V2,• ••, whose span is R°. V10, V1, V2, ..., V10? b. Suppose that we have vectors in R°, v1, V2, ..., V10, whose span is R°. Can every vector b in R° be written uniquely as a linear combination of V1, V2,· ••, V10? С. Do the vectors ei = e2 = ez = cnan m3,
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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Transcribed Image Text:7. Provide a justification for your response to the following questions.
a. Suppose that we have vectors in R°,
Can every vector b in R° be written as a linear combination of
V1, V2,• ••,
whose span is R°.
V10,
V1, V2, ..., V10?
b. Suppose that we have vectors in R°, v1, V2, ..., V10, whose span is R°.
Can every vector b in R° be written uniquely as a linear combination of
V1, V2,· ••,
V10?
С.
Do the vectors
ei =
e2 =
ez =
span R?
438
d. Suppose that v1, v2, ..., Vn span R°. What can you guarantee about
the value of n?
е.
Can 17 vectors in R20 span R"?
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