) Consider the matrix formed by five vectors vj: A = (61 62 63 64 655) = 1 2 0 -1 0 001 3 0 000 0 1 9 in obvious notation. (i) Is the set {vi, V2, V3, V₁, V5} linearly independent (LI)? (ii) Is the set {vi, v₁, vš} LI ? If not, then express 5 as a linear combination of v₁, v4. (iii) Is the set {vi, v2, v3} LI ? If not, write out the dependence relation as a vector equation C₁v₁ + c₂v₂ + C3V3 = 0.
) Consider the matrix formed by five vectors vj: A = (61 62 63 64 655) = 1 2 0 -1 0 001 3 0 000 0 1 9 in obvious notation. (i) Is the set {vi, V2, V3, V₁, V5} linearly independent (LI)? (ii) Is the set {vi, v₁, vš} LI ? If not, then express 5 as a linear combination of v₁, v4. (iii) Is the set {vi, v2, v3} LI ? If not, write out the dependence relation as a vector equation C₁v₁ + c₂v₂ + C3V3 = 0.
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Section4.6: Rank Of A Matrix And Systems Of Linear Equations
Problem 69E: Consider an mn matrix A and an np matrix B. Show that the row vectors of AB are in the row space of...
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![) Consider the matrix formed by five vectors vj:
A = (61 62 63 64 655) =
1 2 0 -1 0
001 3 0
000 0 1
9
in obvious notation.
(i) Is the set {vi, V2, V3, V₁, V5} linearly independent (LI)?
(ii) Is the set {vi, v₁, vš} LI ? If not, then express 5 as a linear combination of v₁, v4.
(iii) Is the set {vi, v2, v3} LI ? If not, write out the dependence relation as a vector equation
C₁v₁ + c₂v₂ + C3V3 = 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F63ed0b59-7e5f-493d-83e4-64fe10b2abd1%2F80803de4-3612-45c7-825f-d35815270684%2F8ickyb_processed.png&w=3840&q=75)
Transcribed Image Text:) Consider the matrix formed by five vectors vj:
A = (61 62 63 64 655) =
1 2 0 -1 0
001 3 0
000 0 1
9
in obvious notation.
(i) Is the set {vi, V2, V3, V₁, V5} linearly independent (LI)?
(ii) Is the set {vi, v₁, vš} LI ? If not, then express 5 as a linear combination of v₁, v4.
(iii) Is the set {vi, v2, v3} LI ? If not, write out the dependence relation as a vector equation
C₁v₁ + c₂v₂ + C3V3 = 0.
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