**Determine whether the given functions are linearly dependent or linearly independent on the specified interval. Justify your decision.**Functions: $\{x^5, x^5 - 1, g\}$ on $(- \infty, \infty)$.---Select the correct choice below and, if necessary, fill in the answer box to complete your choice.- **A.** The functions are linearly dependent because $ c_1 x^5 + c_2 \left(x^5 - 1\right) + c_3 (9) = 0 $ has the solution $ c_1 = $ [box] and $ c_2 = -1 $, and $ c_3 = $ [box]. *(Type integers or simplified fractions.)*- **B.** The functions are linearly independent because $ c_1 x^5 + c_2 \left(x^5 - 1\right) + c_3 (9) = 0 $ has no solutions for constants $ c_1, c_2, $ and $ c_3 $ that are not all zero. *(Select and provide justification based on calculations or known theoretical results.)*

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Description: **Determine whether the given functions are linearly dependent or linearly independent on the specified interval. Justify your decision.**Functions: $\{x^5, x^5 - 1, g\}$ on $(- \infty, \infty)$.---Select the correct choice below and, if necessa

Given x5,x5-1,9 we need to check wheather it is linearly independent or dependent.we know that…

Math

Advanced Math

Determine whether the given functions are linearly dependent or linearly independent on the specified interval. Justify your decision. {x°, x° - 1, 9} on (– 0,00) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The functions are linearly dependent because c,x° + c, (x° - 1) + C3 (9) = 0 has the solution c, = C2 and c, = - 1, and c3 = (Type integers or simplified fractions.) B. The functions are linearly independent because c, x° + c, (x° - 1) + ca (9) = 0 has no solutions for constants c,, c, C4X and C3 that are not all zero.

Determine whether the given functions are linearly dependent or linearly independent on the specified interval. Justify your decision. {x°, x° - 1, 9} on (– 0,00) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The functions are linearly dependent because c,x° + c, (x° - 1) + C3 (9) = 0 has the solution c, = C2 and c, = - 1, and c3 = (Type integers or simplified fractions.) B. The functions are linearly independent because c, x° + c, (x° - 1) + ca (9) = 0 has no solutions for constants c,, c, C4X and C3 that are not all zero.

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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Topic Video

Question

**Determine whether the given functions are linearly dependent or linearly independent on the specified interval. Justify your decision.**

Functions: $\{x^5, x^5 - 1, g\}$ on $(- \infty, \infty)$.

---

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

- **A.** The functions are linearly dependent because $ c_1 x^5 + c_2 \left(x^5 - 1\right) + c_3 (9) = 0 $ has the solution $ c_1 = $ [box] and $ c_2 = -1 $, and $ c_3 = $ [box].

*(Type integers or simplified fractions.)*

- **B.** The functions are linearly independent because $ c_1 x^5 + c_2 \left(x^5 - 1\right) + c_3 (9) = 0 $ has no solutions for constants $ c_1, c_2, $ and $ c_3 $ that are not all zero.

*(Select and provide justification based on calculations or known theoretical results.)*

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