6. Let V₁, V2, V3 € R³ be nonzero such that v3 € (V1, V2), but v2 (v₁). Which of the following is true? (a) V₁, V2, and v3 are coplanar. (b) V₁, V2, and v3 are collinear. (c) V₁, V2, and v3 are linearly independent. (d) v₁, V2, and v3 span R³. 7. Which of the following sets of functions is linearly dependent on R[0,2]? (a) {6, x, sinx} (b) {1, sin x, sin 2x} (c) {cos 2x, sin² x, cos²x} (d) {x, cos x}
6. Let V₁, V2, V3 € R³ be nonzero such that v3 € (V1, V2), but v2 (v₁). Which of the following is true? (a) V₁, V2, and v3 are coplanar. (b) V₁, V2, and v3 are collinear. (c) V₁, V2, and v3 are linearly independent. (d) v₁, V2, and v3 span R³. 7. Which of the following sets of functions is linearly dependent on R[0,2]? (a) {6, x, sinx} (b) {1, sin x, sin 2x} (c) {cos 2x, sin² x, cos²x} (d) {x, cos x}
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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Please help me answer 6 and 7
![6. Let V₁, V2, V3 € R³ be nonzero such that v3 € (V₁, V₂), but v₂ # (v₁). Which of the following is
true?
(a) V₁, V2, and v3 are coplanar.
(b) V₁, V2, and v3 are collinear.
(c) V₁, V2, and v3 are linearly independent. (d) V₁, V2, and v3 span R³.
7. Which of the following sets of functions is linearly dependent on R[0,2π]?
(a) {6, x, sin x}
(b) {1, sin x, sin 2x}
(c) {cos 2x, sin² x, cos²x}
(d) {x, cos x}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F592283d3-70d0-4875-bb5c-b14402919fb7%2F98353370-7f2a-4f18-a2fc-9c1b562d6cec%2F2zzrv3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:6. Let V₁, V2, V3 € R³ be nonzero such that v3 € (V₁, V₂), but v₂ # (v₁). Which of the following is
true?
(a) V₁, V2, and v3 are coplanar.
(b) V₁, V2, and v3 are collinear.
(c) V₁, V2, and v3 are linearly independent. (d) V₁, V2, and v3 span R³.
7. Which of the following sets of functions is linearly dependent on R[0,2π]?
(a) {6, x, sin x}
(b) {1, sin x, sin 2x}
(c) {cos 2x, sin² x, cos²x}
(d) {x, cos x}
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