a4 a1 Let V1 (3).. b4 be four vectors in R³. b₁ b₂ V3 = C1 C2 C4 a1 a2 a3 a4 If we reduce the matrix A = b₁ b₂ b3 b4 to reduced echelon form, we get the following matrix: C1 C2 C3 C4 /1 0 0 3 0 1 0 5 0 0 17, Which one of the following statements must be true? Select one alternative: The set {V₁, V2, V3} is linearly dependent. v4 is a linear combination of V₁, V2₂, and V3 The set {V₁, V2, V3, V4} is linearly independent. V3 is a linear combination of v₁ and v2. = V2 = a2 az b3 C3 V4 =

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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as
a1
Let V₁ =
(3)..
b₁
b₂
b4 be four vectors in R³.
V3 =
C1
C2
C4
a1 a2
a3
a4
If we reduce the matrix A =
b₁ b₂ b3
b4 to reduced echelon form, we get the following matrix:
C1
C2 C3 C4
/1
0 0 3
0
1 0 5
0
0 17,
Which one of the following statements must be true?
Select one alternative:
© The set {V₁, V2, V3} is linearly dependent.
v4 is a linear combination of V₁, V2, and V3
The set {V₁, V2, V3, V4} is linearly independent.
V3 is a linear combination of v₁ and v2.
V2 =
a2
az
b3
C3
V4 =
Transcribed Image Text:as a1 Let V₁ = (3).. b₁ b₂ b4 be four vectors in R³. V3 = C1 C2 C4 a1 a2 a3 a4 If we reduce the matrix A = b₁ b₂ b3 b4 to reduced echelon form, we get the following matrix: C1 C2 C3 C4 /1 0 0 3 0 1 0 5 0 0 17, Which one of the following statements must be true? Select one alternative: © The set {V₁, V2, V3} is linearly dependent. v4 is a linear combination of V₁, V2, and V3 The set {V₁, V2, V3, V4} is linearly independent. V3 is a linear combination of v₁ and v2. V2 = a2 az b3 C3 V4 =
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