Teaching Exam > Teaching Questions > For equation 2x 2y=1 and 2x-y=1 over z3 what ...
Start Learning for Free
For equation 2x 2y=1 and 2x-y=1 over z3 what is the solution?
Most Upvoted Answer
For equation 2x 2y=1 and 2x-y=1 over z3 what is the solution?
Solving Equations over Z3:
To solve the equations 2x 2y=1 and 2x-y=1 over z3, we need to follow the steps given below:
Step 1: Write the Equations
2x + 2y = 1
2x - y = 1
Step 2: Write the Equations in Matrix Form
[2 2 | 1]
[2 -1 | 1]
Step 3: Find the Determinant of the Matrix
det([2 2
2 -1]) = (2*(-1)) - (2*2) = -6 ≡ 0 (mod 3)
Since the determinant is 0 (mod 3), the matrix is singular and the equations have no unique solution.
Step 4: Solve the Equations Using Row Operations
[2 2 | 1]
[2 -1 | 1]
R2 → R2 - R1
[2 2 | 1]
[0 -3 | 0]
R2 → -R2/3
[2 2 | 1]
[0 1 | 0]
R1 → R1 - 2R2
[2 0 | 1]
[0 1 | 0]
Step 5: Write the Solution
The solution to the equations 2x + 2y = 1 and 2x - y = 1 over z3 is:
x ≡ 2 (mod 3)
y ≡ 0 (mod 3)
To solve the equations 2x 2y=1 and 2x-y=1 over z3, we need to follow the steps given below:
Step 1: Write the Equations
2x + 2y = 1
2x - y = 1
Step 2: Write the Equations in Matrix Form
[2 2 | 1]
[2 -1 | 1]
Step 3: Find the Determinant of the Matrix
det([2 2
2 -1]) = (2*(-1)) - (2*2) = -6 ≡ 0 (mod 3)
Since the determinant is 0 (mod 3), the matrix is singular and the equations have no unique solution.
Step 4: Solve the Equations Using Row Operations
[2 2 | 1]
[2 -1 | 1]
R2 → R2 - R1
[2 2 | 1]
[0 -3 | 0]
R2 → -R2/3
[2 2 | 1]
[0 1 | 0]
R1 → R1 - 2R2
[2 0 | 1]
[0 1 | 0]
Step 5: Write the Solution
The solution to the equations 2x + 2y = 1 and 2x - y = 1 over z3 is:
x ≡ 2 (mod 3)
y ≡ 0 (mod 3)
Community Answer
For equation 2x 2y=1 and 2x-y=1 over z3 what is the solution?
( 1,1) and (2,0)
|
Explore Courses for Teaching exam
|
|
For equation 2x 2y=1 and 2x-y=1 over z3 what is the solution?
Question Description
For equation 2x 2y=1 and 2x-y=1 over z3 what is the solution? for Teaching 2024 is part of Teaching preparation. The Question and answers have been prepared according to the Teaching exam syllabus. Information about For equation 2x 2y=1 and 2x-y=1 over z3 what is the solution? covers all topics & solutions for Teaching 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For equation 2x 2y=1 and 2x-y=1 over z3 what is the solution?.
For equation 2x 2y=1 and 2x-y=1 over z3 what is the solution? for Teaching 2024 is part of Teaching preparation. The Question and answers have been prepared according to the Teaching exam syllabus. Information about For equation 2x 2y=1 and 2x-y=1 over z3 what is the solution? covers all topics & solutions for Teaching 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For equation 2x 2y=1 and 2x-y=1 over z3 what is the solution?.
Solutions for For equation 2x 2y=1 and 2x-y=1 over z3 what is the solution? in English & in Hindi are available as part of our courses for Teaching.
Download more important topics, notes, lectures and mock test series for Teaching Exam by signing up for free.
Here you can find the meaning of For equation 2x 2y=1 and 2x-y=1 over z3 what is the solution? defined & explained in the simplest way possible. Besides giving the explanation of
For equation 2x 2y=1 and 2x-y=1 over z3 what is the solution?, a detailed solution for For equation 2x 2y=1 and 2x-y=1 over z3 what is the solution? has been provided alongside types of For equation 2x 2y=1 and 2x-y=1 over z3 what is the solution? theory, EduRev gives you an
ample number of questions to practice For equation 2x 2y=1 and 2x-y=1 over z3 what is the solution? tests, examples and also practice Teaching tests.
|
|
Explore Courses for Teaching exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup