Please help. This problem involves linear independence and bases. Thank you. Problem 17.a) Determine if B = {sin(2x + ), cos² (x), sin²(x), sin(x), sin (x), e"} is alinearly independent set.b) Determine if Blinearly independent set.{cos(2r + ), cos²(x), sin²(x), sin(x), sin³ (x), 1} is ac) Determine if B = {1, x, e"} is a linearly independent set.

Name: Please help. This problem involves linear independence and bases. Than
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Description: Please help. This problem involves linear independence and bases. Thank you. Problem 17.a) Determine if B = {sin(2x + ), cos² (x), sin²(x), sin(x), sin (x), e"} is alinearly independent set.b) Determine if Blinearly independent set.{cos(2r + ), cos²(

Answered: a) Determine if B = {sin(2a + ), cos²…

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. This problem involves linear independence and bases. Thank you.

Problem 17.
a) Determine if B = {sin(2x + ), cos² (x), sin²(x), sin(x), sin (x), e"} is a
linearly independent set.
b) Determine if B
linearly independent set.
{cos(2r + ), cos²(x), sin²(x), sin(x), sin³ (x), 1} is a
c) Determine if B = {1, x, e"} is a linearly independent set.

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A set of vectors ${v_{1}, v_{2}, v_{3 . . . . . .} v_{n}}$ is said to be linearly independent if their exists scalars $a_{1}, a_{2}, . . . . . . . . a_{n}$ are all zero such that $a_{1} v_{1} + a_{2} v_{2} + . . . . . . . a_{n} v_{n} = 0$ .

A set of vectors ${v_{1}, v_{2}, v_{3 . . . . . .} v_{n}}$ is said to be linearly dependent if their exists scalars $a_{1}, a_{2}, . . . . . . . . a_{n}$ not all zero such that $a_{1} v_{1} + a_{2} v_{2} + . . . . . . . a_{n} v_{n} = 0$ .

Another definition of linearly dependent is that if one of the vectors can be expressed in terms of other which results in less spanning potential. If spanning potential remains unchanged in that case set is linearly independent.

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