Use the properties of vector addition and scalar multiplication from the following theorem. Properties of Vector Addition and Scalar Multiplication in R" Let u, v, and w be vectors in R", and let c and d be scalars. 1. u + v is a vector in R". 2. u + v = v + u Closure under addition Commutative property of addition Associative property of addition Additive identity property Additive inverse property Closure under scalar multiplication Distributive property Distributive property Associative property of multiplication Multiplicative identity property 3. (u + v) + w = u + (v + w) 4. u + 0 = u 5. u + (-u) = 0 6. cu is a vector in R". 7. cu + v) = cu + cv 8. (c + d)u = cu + du 9. c(du) = (cd)u 10. 1(u) = u Step Justification -(-v) + (-v) = 0 and v + (-v) = 0 distributive property -(-v) + (-v) = v + (-v) transitive property of equality -(-v) + (-v) + v = v + (-v) + v associative property of addition -(-v) + ((-v) + v) = v + ((-v) + v) distributive property |-(-v) + 0 = v + 0 distributive property -(-v) = v multiplicative identity property X X
Use the properties of vector addition and scalar multiplication from the following theorem. Properties of Vector Addition and Scalar Multiplication in R" Let u, v, and w be vectors in R", and let c and d be scalars. 1. u + v is a vector in R". 2. u + v = v + u Closure under addition Commutative property of addition Associative property of addition Additive identity property Additive inverse property Closure under scalar multiplication Distributive property Distributive property Associative property of multiplication Multiplicative identity property 3. (u + v) + w = u + (v + w) 4. u + 0 = u 5. u + (-u) = 0 6. cu is a vector in R". 7. cu + v) = cu + cv 8. (c + d)u = cu + du 9. c(du) = (cd)u 10. 1(u) = u Step Justification -(-v) + (-v) = 0 and v + (-v) = 0 distributive property -(-v) + (-v) = v + (-v) transitive property of equality -(-v) + (-v) + v = v + (-v) + v associative property of addition -(-v) + ((-v) + v) = v + ((-v) + v) distributive property |-(-v) + 0 = v + 0 distributive property -(-v) = v multiplicative identity property X X
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:Use the properties of vector addition and scalar multiplication from the following theorem.
Properties of Vector Addition and Scalar Multiplication in R"
Let u, v, and w be vectors in R", and let c and d be scalars.
1. u + v is a vector in R".
2. u + v = v + u
Closure under addition
Commutative property of addition
Associative property of addition
Additive identity property
Additive inverse property
Closure under scalar multiplication
Distributive property
Distributive property
Associative property of multiplication
Multiplicative identity property
3. (u + v) + w = u + (v + w)
4. u + 0 = u
5. u + (-u) = 0
6. cu is a vector in R".
7. c(u + v) = cu + cv
8. (c + d)u = cu + du
9. c(du) = (cd)u
10. 1(u) = u
Step
Justification
-(-v) + (-v) = 0 and v + (-v) = 0
distributive property
-(-v) + (-v) = v + (-v)
transitive property of equality
-(-v) + (-v) + v = v + (-v) + v
associative property of addition
-(-v) + ((-v) + v) = v + ((-v) + v) distributive property
-(-v) + 0 = v + 0
distributive property
-(-v) = v
multiplicative identity property
X X
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
