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Using matrix inversion method,solve the following system of equation for x,y&z X+ Y+ Z=5. 2x Y-Z=2. 2X-Y Z= 2?
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Using matrix inversion method,solve the following system of equation f...
System of Equations
The given system of equations is:
1. X + Y + Z = 5
2. 2X + Y - Z = 2
3. 2X - Y + Z = 2
Matrix Representation
We can represent this system in matrix form as AX = B, where:
- A =
| 1 1 1 |
| 2 1 -1 |
| 2 -1 1 |
- X =
| X |
| Y |
| Z |
- B =
| 5 |
| 2 |
| 2 |
Finding the Inverse of Matrix A
To solve for X, we need to find the inverse of matrix A (denoted as A^(-1)) and then multiply it by B.
1. Calculate the determinant of A.
2. Find the matrix of minors, then cofactors, and finally the adjugate of A.
3. Divide the adjugate by the determinant to find A^(-1).
Calculating X
Once we have A^(-1):
- Use the formula: X = A^(-1)B.
Final Calculation
After performing the matrix multiplication:
- X = A^(-1)B will yield the values for X, Y, and Z.
Conclusion
The values of X, Y, and Z obtained from the above calculations will be the solution to the system of equations. This method is efficient for solving linear equations and highlights the importance of matrix operations in algebra.
The given system of equations is:
1. X + Y + Z = 5
2. 2X + Y - Z = 2
3. 2X - Y + Z = 2
Matrix Representation
We can represent this system in matrix form as AX = B, where:
- A =
| 1 1 1 |
| 2 1 -1 |
| 2 -1 1 |
- X =
| X |
| Y |
| Z |
- B =
| 5 |
| 2 |
| 2 |
Finding the Inverse of Matrix A
To solve for X, we need to find the inverse of matrix A (denoted as A^(-1)) and then multiply it by B.
1. Calculate the determinant of A.
2. Find the matrix of minors, then cofactors, and finally the adjugate of A.
3. Divide the adjugate by the determinant to find A^(-1).
Calculating X
Once we have A^(-1):
- Use the formula: X = A^(-1)B.
Final Calculation
After performing the matrix multiplication:
- X = A^(-1)B will yield the values for X, Y, and Z.
Conclusion
The values of X, Y, and Z obtained from the above calculations will be the solution to the system of equations. This method is efficient for solving linear equations and highlights the importance of matrix operations in algebra.
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Using matrix inversion method,solve the following system of equation for x,y&z X+ Y+ Z=5. 2x Y-Z=2. 2X-Y Z= 2?
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Using matrix inversion method,solve the following system of equation for x,y&z X+ Y+ Z=5. 2x Y-Z=2. 2X-Y Z= 2? for B Com 2025 is part of B Com preparation. The Question and answers have been prepared according to the B Com exam syllabus. Information about Using matrix inversion method,solve the following system of equation for x,y&z X+ Y+ Z=5. 2x Y-Z=2. 2X-Y Z= 2? covers all topics & solutions for B Com 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Using matrix inversion method,solve the following system of equation for x,y&z X+ Y+ Z=5. 2x Y-Z=2. 2X-Y Z= 2?.
Using matrix inversion method,solve the following system of equation for x,y&z X+ Y+ Z=5. 2x Y-Z=2. 2X-Y Z= 2? for B Com 2025 is part of B Com preparation. The Question and answers have been prepared according to the B Com exam syllabus. Information about Using matrix inversion method,solve the following system of equation for x,y&z X+ Y+ Z=5. 2x Y-Z=2. 2X-Y Z= 2? covers all topics & solutions for B Com 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Using matrix inversion method,solve the following system of equation for x,y&z X+ Y+ Z=5. 2x Y-Z=2. 2X-Y Z= 2?.
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