6. Let V₁, V2, V3 R³ be nonzero such that v3 E (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. (d) v₁, v2, and v3 span R³. (c) v₁, V2, and v3 are linearly independent. 7. Which of the following sets of functions is linearly dependent on R[0,2]? (a) {6, x, sin x) (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 E (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. (d) v₁, v2, and v3 span R³. (c) v₁, V2, and v3 are linearly independent. 7. Which of the following sets of functions is linearly dependent on R[0,2]? (a) {6, x, sin x) (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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![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, 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%2Fefa6c0fe-4d2f-45fd-9345-a33ad1509aee%2F6941b971-63ce-4160-95d0-9b7966569be1%2Fi9sjq5n_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[0,2]?
(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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