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onil s 2 S = {v1,V2} = 4 5 7 8. a. Explain why S is linearly independent but is not a basis for R³. b. Find a vector v3 e R3 that you can append to S to form a new set of vectors S' = {v1, V2, V3} %3D that is a basis for R3. (Hint: There are infinitely many possibilities for V3. Perhaps you can just guess at one and then check that it works.)

onil s 2 S = {v1,V2} = 4 5 7 8. a. Explain why S is linearly independent but is not a basis for R³. b. Find a vector v3 e R3 that you can append to S to form a new set of vectors S' = {v1, V2, V3} %3D that is a basis for R3. (Hint: There are infinitely many possibilities for V3. Perhaps you can just guess at one and then check that it works.)

Advanced Engineering Mathematics
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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2 S = {v1,V2} 4 || %3D 8. a. Explain why S is linearly independent but is not a basis for R3. b. Find a vector v3 e R3 that you can append to S to form a new set of vectors S' = {v1,V2, V3} %3D that is a basis for R3. (Hint: There are infinitely many possibilities for V3. Perhaps you can just guess at one and then check that it works.)
Transcribed Image Text:2 S = {v1,V2} 4 || %3D 8. a. Explain why S is linearly independent but is not a basis for R3. b. Find a vector v3 e R3 that you can append to S to form a new set of vectors S' = {v1,V2, V3} %3D that is a basis for R3. (Hint: There are infinitely many possibilities for V3. Perhaps you can just guess at one and then check that it works.)
9. In R3, let S be the set of vectors
Transcribed Image Text:9. In R3, let S be the set of vectors
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