1 2 Consider the column vectors vị = V2 = -1 and v3 = -1 1 (a) Use row operations on an appropriate matrix to show that these three vectors are not linearly independent. (b) Write v3 as a linear combination of vi and v2. (That is, find constants ki and k2 such that v3 = kiV1 + k2v2). (c) Explain why {v1, V2, V3} is not a basis for R3.
1 2 Consider the column vectors vị = V2 = -1 and v3 = -1 1 (a) Use row operations on an appropriate matrix to show that these three vectors are not linearly independent. (b) Write v3 as a linear combination of vi and v2. (That is, find constants ki and k2 such that v3 = kiV1 + k2v2). (c) Explain why {v1, V2, V3} is not a basis for R3.
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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Consider the column vectors v1 =
• V2 =
-1
and v3 =
1
-2
(a) Use row operations on an appropriate matrix to show that these three vectors are not linearly independent.
(b) Write v3 as a linear combination of v1 and v2. (That is, find constants k1 and k2 such that v3 = kịv1+ k2v2).
(c) Explain why {v1, v2, V3} is not a basis for R3.
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