2023
MAT1503
Assignment 3
(692080)
DUE: 26 June 2023 at 2:00PM
UnisaGuides
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The study notes provided herein are intended to assist students in their academic endeavours and
provide guidance based on assignments. However, it is important to understand and acknowledge
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should be used as a tool for learning and inspiration, but any direct reproduction of the content
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or misuse of the information provided.
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,Given,
If the determinant of the matrix is zero,
it implies that the three rows of the matrix are linearly dependent, meaning that one row
can be expressed as a linear combination of the other two rows
In terms of points, this means that the three points (a, b), (c, d), and (e, f) lie on the same
line.
Expand the determinant of the matrix using the first row:
Simplifying the expression
Rearrange the terms to group the variables
The equationa(d−f)+b(e−c)+c(f−d)=0 implies that the three terms are equal to zero, which
means that the three expressions (d−f),(e−c),and(f−d)are all zero
Since each of these expressions evaluates to zero, it implies that d=f,e=c,andf=d This
shows that the points (a,b),(c,d),and(e,f) lie on the same line, making them collinear.
hence, we have proved that points (a, b), (c, d), and (e, f) are collinear whenever the
determinant of the matrix is equal to zero.
Explanation:
we used the concept of linear dependence
, slope=b₂−b₁/a₂−a₁
Then, using the point-slope form of the equation of a line, we have:
y−b₁=slope×(x−a₁)
y=slope×(x−a₁)+b₁
Substituting the value of the slope, the equation becomes
y=(b₂−b₁/a₂−a₁)×(x−a₁)+b₁
This is the equation of the line passing through the distinct points (a₁, b₁) and (a₂, b₂)
Explanation:
Using the slope formula we find the slope and then putting all value in the equation
MAT1503
Assignment 3
(692080)
DUE: 26 June 2023 at 2:00PM
UnisaGuides
, Disclaimer
The study notes provided herein are intended to assist students in their academic endeavours and
provide guidance based on assignments. However, it is important to understand and acknowledge
the following points before utilizing these study notes:
1. Educational Aid: These study notes are designed to serve as educational aids and should not be
considered as a substitute for individual research, critical thinking, or professional guidance. Students
are encouraged to conduct their own extensive research and consult with their instructors or
academic advisors for specific assignment requirements.
2. Personal Responsibility: While every effort has been made to ensure the accuracy and reliability of
the information provided in these study notes, the seller cannot guarantee the completeness or
correctness of all the content. It is the responsibility of the buyer to verify the accuracy of the
information and use their own judgment when applying it to their assignments.
3. Academic Integrity: It is crucial for students to uphold academic integrity and adhere to their
institution's policies and guidelines regarding plagiarism, citation, and referencing. These study notes
should be used as a tool for learning and inspiration, but any direct reproduction of the content
without proper acknowledgment and citation may constitute academic misconduct.
4. Subject Variation: The study notes may not cover all possible variations or interpretations of a
subject matter. Different institutions, professors, or courses may have specific requirements or
perspectives that are not addressed in these notes. Therefore, it is essential for students to tailor
their assignments according to their unique academic environment.
5. Limited Liability: The seller of these study notes shall not be held liable for any direct or indirect
damages, losses, or consequences arising from the use of the notes. This includes, but is not limited
to, poor grades, academic penalties, or any other negative outcomes resulting from the application
or misuse of the information provided.
By purchasing and utilizing these study notes, you acknowledge that you have read, understood, and
agreed to the above disclaimer. It is recommended to review the disclaimer periodically, as it may be
subject to updates or revisions without prior notice.
,Given,
If the determinant of the matrix is zero,
it implies that the three rows of the matrix are linearly dependent, meaning that one row
can be expressed as a linear combination of the other two rows
In terms of points, this means that the three points (a, b), (c, d), and (e, f) lie on the same
line.
Expand the determinant of the matrix using the first row:
Simplifying the expression
Rearrange the terms to group the variables
The equationa(d−f)+b(e−c)+c(f−d)=0 implies that the three terms are equal to zero, which
means that the three expressions (d−f),(e−c),and(f−d)are all zero
Since each of these expressions evaluates to zero, it implies that d=f,e=c,andf=d This
shows that the points (a,b),(c,d),and(e,f) lie on the same line, making them collinear.
hence, we have proved that points (a, b), (c, d), and (e, f) are collinear whenever the
determinant of the matrix is equal to zero.
Explanation:
we used the concept of linear dependence
, slope=b₂−b₁/a₂−a₁
Then, using the point-slope form of the equation of a line, we have:
y−b₁=slope×(x−a₁)
y=slope×(x−a₁)+b₁
Substituting the value of the slope, the equation becomes
y=(b₂−b₁/a₂−a₁)×(x−a₁)+b₁
This is the equation of the line passing through the distinct points (a₁, b₁) and (a₂, b₂)
Explanation:
Using the slope formula we find the slope and then putting all value in the equation
