Determine whether the set, together with the indicated operations, is a vector space. If it is not, then identify one of the vector space axioms that fails. The set of all 4 x 4 matrices of the form осса bo ca a bo c a b b 1 with the standard operations O The set is a vector space. O The set is not a vector space because it is not closed under addition. O The set is not a vector space because it does not satisfy the associative property of addition. O The set is not a vector space because a scalar identity does not exist. O The set is not a vector space because it does not satisfy the distributive property.
Determine whether the set, together with the indicated operations, is a vector space. If it is not, then identify one of the vector space axioms that fails. The set of all 4 x 4 matrices of the form осса bo ca a bo c a b b 1 with the standard operations O The set is a vector space. O The set is not a vector space because it is not closed under addition. O The set is not a vector space because it does not satisfy the associative property of addition. O The set is not a vector space because a scalar identity does not exist. O The set is not a vector space because it does not satisfy the distributive property.
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:Determine whether the set, together with the indicated operations, is a vector space. If it is not, then identify one of the vector space axioms that fails.
The set of all 4 x 4 matrices of the form
0 сса
bo ca
a b o c
a b b 1
with the standard operations
O The set is a vector space.
O The set is not a vector space because it is not closed under addition.
O The set is not a vector space because it does not satisfy the associative property of addition.
O The set is not a vector space because a scalar identity does not exist.
O The set is not a vector space because it does not satisfy the distributive property.
Transcribed Image Text:Use a software program or a graphing utility with matrix capabilities to write v as a linear combination of u1, u2, U3, U4, and ug. Then verify your solution.
v = (6, 8, 7, –2, 3)
u1 = (1, 1, -1, 2, 1)
u2 = (2, 1, 2, -1, 1)
Из %3D (1, 2, 0, 1, 2)
U4 = (0, 2, 0, 1, -4)
u5 = (1, 1, 2, -1, 2)
Juz + (
Jus + (
Jus
V =
+
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