Gaussian Elimination
Gaussian Elimination is a fundamental method in linear algebra used to solve systems of linear equations and to find the inverse of a matrix. It operates by transforming the augmented matrix of the system into its reduced row-echelon form through a sequence of elementary row operations. This process simplifies the system, making it easier to identify solutions or determine inconsistency. With its applications spanning various fields such as engineering, physics, and computer science, Gaussian Elimination serves as a cornerstone technique for solving complex mathematical problems efficiently and accurately.
Questions
- How do you solve using gaussian elimination or gauss-jordan elimination, #y + 3z = 6#, #x + 2y + 4z = 9#, #2x + y + 6z = 11#?
- How do you solve using gaussian elimination or gauss-jordan elimination, # 2x - y + 3z = 24#, #2y - z = 14#, #7x - 5y = 6#?
- How do you solve using gaussian elimination or gauss-jordan elimination, #2x+y-z+2w=-6#, #3x+4y+w=1#, #x+5y+2z+6w=-3#, #5x+2y-z-w=3#?
- How do you solve the system #3x+2y-3z=-2#, #7x-2y+5z=-14#, #2x+4y+z=6#?
- How do you solve using gaussian elimination or gauss-jordan elimination, #2x_1 + 2x_2 + 2x_3 = 0#, #-2x_1 + 5x_2 + 2x_3 = 0#, #-7x_1 + 7x_2 + x_3 = 0#?
- How do you solve using gaussian elimination or gauss-jordan elimination, #3x + 4y -7z + 8w =0#, #4x +2y+ 8w = 12#, #10x -12y +6z +14w=5#?
- How do you solve using gaussian elimination or gauss-jordan elimination, #4x_1 + 5x_2 + 2x_3 = 11#, #2x_2 + 3x_3 - 4x_4 = -2#, #2x_1 + x_2 + 3x_4 = 12#, #x_1 + x_3 + x_4 = 9#?
- How do you solve using gaussian elimination or gauss-jordan elimination, #6x+10y=10#, #x+2y=5#?
- How do you solve using gaussian elimination or gauss-jordan elimination, #-x+y-z=1#, #-x+3y+z=3#, #x+2y+4z=2#?
- How do you solve using gaussian elimination or gauss-jordan elimination, #x +2y +3z = 1#, #2x +5y +7z = 2#, #3x +5y +7z = 4#?
- How do you solve using gaussian elimination or gauss-jordan elimination, #x+3y+z=7#, #x+y+4z=18#, #-x-y+z=7#?
- How do you solve using gaussian elimination or gauss-jordan elimination, #x-2y-z=2#, #2x-y+z=4#, #-x+y-2z=-4#?
- How do you solve using gaussian elimination or gauss-jordan elimination, #3y + 2z = 4#, #2x − y − 3z = 3#, #2x+ 2y − z = 7#?
- How do you solve using gaussian elimination or gauss-jordan elimination, #-2x-5y=-15#, #-6x-15y=-45#?
- How do you solve using gaussian elimination or gauss-jordan elimination, #X- 3Y + 2Z = -5#, #4X - 11Y + 4Z = -7#, #3X - 8Y + 2Z = -2#?
- How do you solve using gaussian elimination or gauss-jordan elimination, #X + 2Y- 2Z=1#, #2X + 3Y + Z=14#, #4Y + 5Z=27#?
- How do you solve using gaussian elimination or gauss-jordan elimination, #x_1 + 3x_2 +x_3 + x_4= 3#, #2x_1- 2x_2 + x_3 + 2x_4 =8# and #3x_1 + x_2 + 2x_3 - x_4 =-1#?
- How do you solve the system #y - 2 z = - 6#, #- 4x + y + 4 z = 44#, #- 4 x + 2 z = 30#?
- How do you solve using gaussian elimination or gauss-jordan elimination, #x_1 + 2x_2+ 4x_3= 6#, #x_1+ x_2 + 2x_3= 3#?
- How do you solve using gaussian elimination or gauss-jordan elimination, #x_1 + 2x_2 − 4x_3 − x_4 = 7#, #2x_1 + 5x_2 − 9x_3 − 4x_4 =16#, #x_1 + 5x_2 − 7x_3 − 7x_4 = 13#?