Let V₁, V2, V3 be the vectors in R³ defined by 16 11 3 12 34 (a) Is {V₁, V₂, V3} linearly independent? Write all zeros if it is or if it is linearly dependent write zero as a non-trivial (not all zero coefficients) linear combination of V₁, V₂, and v3 v₁+ (c) Type the dimension of span{v₁, v2, v3}: 0= Note: You can earn partial credit on this problem. V1 = v2 = 0= V3 = (b) Is (v₁, v₂} linearly independent? Write all zeros if it is or if it is linearly dependent write zero as a non-trivial (not all zero coefficients) linear combination of v₁ and v₂. v1+ 16 H 19 -10 v2+ V3 V2

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Let V₁, V2, V3 be the vectors in R³ defined by
16
-0-0-0
3
=
V3
34
(a) Is {V₁, V2, V3} linearly independent? Write all zeros if it is or if it is linearly dependent write zero as a non-trivial (not all zero coefficients) linear combination of V₁, V2, and v3
(c) Type the dimension of span{V₁, V2, V3}:|
0 =
Note: You can earn partial credit on this problem.
V1 =
16
11
12
v₁+
0 =
V2+
(b) Is {v₁, v₂} linearly independent? Write all zeros if it is or if it is linearly dependent write zero as a non-trivial (not all zero coefficients) linear combination of v₁ and v₂.
v₁+
16
19
V3
V2
Transcribed Image Text:Let V₁, V2, V3 be the vectors in R³ defined by 16 -0-0-0 3 = V3 34 (a) Is {V₁, V2, V3} linearly independent? Write all zeros if it is or if it is linearly dependent write zero as a non-trivial (not all zero coefficients) linear combination of V₁, V2, and v3 (c) Type the dimension of span{V₁, V2, V3}:| 0 = Note: You can earn partial credit on this problem. V1 = 16 11 12 v₁+ 0 = V2+ (b) Is {v₁, v₂} linearly independent? Write all zeros if it is or if it is linearly dependent write zero as a non-trivial (not all zero coefficients) linear combination of v₁ and v₂. v₁+ 16 19 V3 V2
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