Let v₁. V₂. V3 be the vectors in R³ defined by --8-8-8 (a) is {V1, V2, V3} linearly independent? Write all zeros if it is, or if it is linearly dependent write the zero vector as a non-trivial (not all zero coefficients) linear combination of V₁, V2, and V3 = 10 (c) Type the dimension of span {V₁, V2, V3} 18 V3 0= =v₁+√₂+√3 (b) is {V1, V2} linearly independent? Write all zeros if it is, or if it is linearly dependent write the zero vector as a non-trivial (not all zero coefficients) linear combination of v₁ and v₂. 0=v₁+0v₂ V2 7 V3
Let v₁. V₂. V3 be the vectors in R³ defined by --8-8-8 (a) is {V1, V2, V3} linearly independent? Write all zeros if it is, or if it is linearly dependent write the zero vector as a non-trivial (not all zero coefficients) linear combination of V₁, V2, and V3 = 10 (c) Type the dimension of span {V₁, V2, V3} 18 V3 0= =v₁+√₂+√3 (b) is {V1, V2} linearly independent? Write all zeros if it is, or if it is linearly dependent write the zero vector as a non-trivial (not all zero coefficients) linear combination of v₁ and v₂. 0=v₁+0v₂ V2 7 V3
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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Transcribed Image Text:Let V₁, V₂, V3 be the vectors in R³ defined by
-8-8-0
V2-=
10
(c) Type the dimension of span{v1, V2, V3}:
18
(a) Is {V₁, V2, V3} linearly independent? Write all zeros if it is, or if it is linearly dependent write the zero vector as a non-trivial (not all zero coefficients) linear combination of V1, V2, and v3
0=
V₁+
vet
0-
7
V3
(b) Is (v1, v₂} linearly independent? Write all zeros if it is, or if it is linearly dependent write the zero vector as a non-trivial (not all zero coefficients) linear combination of v₁ and v2.
°=v₁+v₂
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