Written by students who passed Immediately available after payment Read online or as PDF Wrong document? Swap it for free 4.6 TrustPilot
logo-home
logo
  • University Of South Africa (Unisa)
  • MAT2611 - Linear Algebra (MAT2611)
To add items to your wishlist, you must be logged in
Document preview thumbnail
Preview 1 out of 9 pages
Other

MAT2611 Assignment TWO of 2023

0.0
(0 reviews)
- sold
9 pages
2022/2023 Written for academic year
Institution
University Of South Africa (Unisa)
Course
MAT2611 - Linear Algebra (MAT2611)
Document preview thumbnail
Preview 1 out of 9 pages

UNISA Linear Algebra MAT2611 Assignment TWO of 2023 solutions.

Content preview

MAT2611 ASSIGNMENT 1 2023


Problem 3

𝑉 = ℝ2

𝒖 = (𝑢1 , 𝑢2 ), 𝒗 = (𝑣1 , 𝑣2 ) ∈ 𝑉

𝒖 + 𝒗 = (𝑢1 + 𝑣1 − 1, 𝑢2 + 𝑣2 − 1)

𝑘𝒖 = (𝑘𝑢1 , 𝑘𝑢2 ) 𝑘∈ℝ

(a)

𝒖 = (1, −2), 𝒗 = (3, 0), 𝑘=4

𝒖 + 𝒗 = (1 + 3 − 1, −2 + 0 − 1)

𝒖 + 𝒗 = (4 − 1, −2 − 1)

𝒖 + 𝒗 = (3, −3)


𝑘𝒖 + (−𝒗) = 4(1, −2) + (−1)(3, 0)

𝑘𝒖 + (−𝒗) = (4 × 1, 4 × −2) + (−1 × 3, −1 × 0)

𝑘𝒖 + (−𝒗) = (4, −8) + (−3, 0)

𝑘𝒖 + (−𝒗) = (4 + (−3) − 1, −8 + 0 − 1)

𝑘𝒖 + (−𝒗) = (1 − 1, −8 − 1)

𝑘𝒖 + (−𝒗) = (0, −9)

(b)

Let 𝒖 = (𝑢1 , 𝑢2 )

𝒖 + (0, 0) = (𝑢1 , 𝑢2 ) + (0, 0)

𝒖 + (0, 0) = (𝑢1 + 0 − 1, 𝑢2 + 0 − 1)

𝒖 + (0, 0) = (𝑢1 − 1, 𝑢2 − 1)

𝒖 + (0, 0) ≠ (𝑢1 , 𝑢2 )

𝒖 + (0, 0) ≠ 𝒖

Similarly, (0, 0) + 𝒖 ≠ 𝒖

Document information

Uploaded on
April 3, 2023
Number of pages
9
Written in
2022/2023
Type
Other
Person
Unknown
Report Copyright Violation
$10.64
Wrong document? Swap it for free Within 14 days of purchase and before downloading, you can choose a different document. You can simply spend the amount again.
Written by students who passed
Immediately available after payment
Read online or as PDF
Seller avatar
Reputation scores are based on the amount of documents a seller has sold for a fee and the reviews they have received for those documents. There are three levels: Bronze, Silver and Gold. The better the reputation, the more your can rely on the quality of the sellers work.
lyzo2005
4.2
(145)
Sold
733
Followers
372
Items
102
Last sold
11 months ago

Browse related subjects

Subjects

  • mat2611
  • linear algebra
  • unisa

Why students choose Stuvia

Created by fellow students, verified by reviews

Quality you can trust: written by students who passed their tests and reviewed by others who've used these notes.

Didn't get what you expected? Choose another document

No worries! You can instantly pick a different document that better fits what you're looking for.

Pay as you like, start learning right away

No subscription, no commitments. Pay the way you're used to via credit card and download your PDF document instantly.

Student with book image

“Bought, downloaded, and aced it. It really can be that simple.”

Alisha Student

Working on your references?

Create accurate citations in APA, MLA and Harvard with our free citation generator.

Learn more Create citation
Working on your references?

Frequently asked questions