UPSC Exam > UPSC Questions > Solve the following set of equations by Matri...
Start Learning for Free
Solve the following set of equations by Matrix inversion method
3x + 2y - 5z = 12
3y +4z - 2 = 0
z -x +2y = 2?
3x + 2y - 5z = 12
3y +4z - 2 = 0
z -x +2y = 2?
Most Upvoted Answer
Solve the following set of equations by Matrix inversion method 3x + 2...
Matrix Inversion Method to Solve a Set of Equations
Step 1: Write the Equations in Matrix Form
Given equations:
3x + 2y - 5z = 12
3y + 4z - 2 = 0
z - x + 2y = 2
Rewriting the equations in matrix form:
AX = B
Where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix.
A =
| 3 2 -5 |
| 0 3 4 |
| -1 2 1 |
X =
| x |
| y |
| z |
B =
| 12 |
| 2 |
| 2 |
Step 2: Find the Inverse of Matrix A
To solve for X, we need to find the inverse of matrix A:
A^-1 = 1/det(A) * adj(A)
Where det(A) is the determinant of A and adj(A) is the adjugate of A.
Step 3: Calculate the Determinant and Adjugate of Matrix A
det(A) = 3(3*1 - 2*4) - 2(0*1 - 4*(-1)) + (-5)(0*2 - 3*(-1))
det(A) = 3(3 - 8) - 2(0 + 4) + (-5)(0 + 3)
det(A) = 3(-5) - 2(4) - 5(3)
det(A) = -15 - 8 - 15
det(A) = -38
adj(A) =
| 3 4 11 |
| 5 -5 -3 |
| -2 3 -6 |
Step 4: Find the Inverse of Matrix A
A^-1 = 1/-38 * adj(A)
A^-1 =
| -3/38 -4/38 -11/38 |
| -5/38 5/38 3/38 |
| 2/38 -3/38 6/38 |
Step 5: Solve for X
X = A^-1 * B
X =
| -3/38 -4/38 -11/38 | | 12 |
| -5/38 5/38 3/38 | * | 2 |
| 2/38 -3/38 6/38 | | 2 |
Solving the matrix multiplication, we get the values of x, y, and z.
Therefore, x = -2, y = 3, z = 4.
This is how the set of equations is solved using the Matrix Inversion method.
Attention UPSC Students!
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.
|
Explore Courses for UPSC exam
|
|
Similar UPSC Doubts
Top Courses for UPSCView all
Solve the following set of equations by Matrix inversion method 3x + 2y - 5z = 12 3y +4z - 2 = 0 z -x +2y = 2?
Question Description
Solve the following set of equations by Matrix inversion method 3x + 2y - 5z = 12 3y +4z - 2 = 0 z -x +2y = 2? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Solve the following set of equations by Matrix inversion method 3x + 2y - 5z = 12 3y +4z - 2 = 0 z -x +2y = 2? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solve the following set of equations by Matrix inversion method 3x + 2y - 5z = 12 3y +4z - 2 = 0 z -x +2y = 2?.
Solve the following set of equations by Matrix inversion method 3x + 2y - 5z = 12 3y +4z - 2 = 0 z -x +2y = 2? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Solve the following set of equations by Matrix inversion method 3x + 2y - 5z = 12 3y +4z - 2 = 0 z -x +2y = 2? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solve the following set of equations by Matrix inversion method 3x + 2y - 5z = 12 3y +4z - 2 = 0 z -x +2y = 2?.
Solutions for Solve the following set of equations by Matrix inversion method 3x + 2y - 5z = 12 3y +4z - 2 = 0 z -x +2y = 2? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of Solve the following set of equations by Matrix inversion method 3x + 2y - 5z = 12 3y +4z - 2 = 0 z -x +2y = 2? defined & explained in the simplest way possible. Besides giving the explanation of
Solve the following set of equations by Matrix inversion method 3x + 2y - 5z = 12 3y +4z - 2 = 0 z -x +2y = 2?, a detailed solution for Solve the following set of equations by Matrix inversion method 3x + 2y - 5z = 12 3y +4z - 2 = 0 z -x +2y = 2? has been provided alongside types of Solve the following set of equations by Matrix inversion method 3x + 2y - 5z = 12 3y +4z - 2 = 0 z -x +2y = 2? theory, EduRev gives you an
ample number of questions to practice Solve the following set of equations by Matrix inversion method 3x + 2y - 5z = 12 3y +4z - 2 = 0 z -x +2y = 2? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
Suggested Free Tests
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