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    17. Solve the system of equations by the Gaussian elimination method.
    x- 3y + z= 8
    2x- 5y -3 z= 2
    x + 4y + z= 1

    18. Find the inverse of the given matrix.
    1 2
    -2 -3

    19. Evaluate the determinant by expanding by cofactors.
    -2 3 2
    1 2 -3
    -4 -2 1

    20. Solve the system of equations by using Cramer's Rule.
    2x + 5 y= 9
    5x + 7y =8

    © BrainMass Inc. brainmass.com October 2, 2022, 2:30 pm ad1c9bdddf
    https://brainmass.com/math/matrices/solve-system-equations-gaussian-elimination-method-5111

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    SOLUTION This solution is FREE courtesy of BrainMass!

    17. Solve the system of equations by the Gaussian elimination method.

    x- 3y + z= 8 -------------1
    2x- 5y -3 z= 2 -----------2
    x + 4y + z= 1 ------------3

    Eliminate x from equation 2 and 3

    Equation 2 - 2 Equation 1 is
    (2x- 5y -3 z= 2 ) - 2 (x- 3y + z= 8)
    or y-5z= -14 -----new equation 2

    Equation 3 -Equation 1 is
    (x + 4y + z= 1) -(x- 3y + z= 8)
    or 7y = -7
    0r y= -1 new equation 3

    Substituting this value of y in new equation 2
    y-5z= -14
    -1-5z=-14
    0r -5z=-13
    0r z=-13/-5=2.6

    y=-1
    z=2.6
    Substituting these values in Equation 1
    x- 3y + z= 8
    x-3(-1)+2.6=8
    x=8-3-2.6=2.4

    x=2.4
    y=-1
    z=2.6
    Answer

    18. Find the inverse of the given matrix.

    elements of Inverse of a matrix = (cofactor of ajk in determinant of A) / det [A]

    Determinant of matrix= (1* -3)-(2*-2)=-3+4=1
    Cofactor of 1 is -3
    Cofactor of 2 is -(-2)=2
    Cofactor of -2 is -(2)=-2
    Cofactor of -3 is 1

    Inverse = 1/ det [A] * |-3 2|
    |-2 1 |
    =1/1 * |-3 2 |
    | -2 1|

    Inverse of the matrix
    =|-3 2 |
    | -2 1|

    19. Evaluate the determinant by expanding by cofactors.

    Determinant of matrix=
    + (-2) * {(2* 1)-(-3*-2) } - (3) * {(1* 1)-(-3*-4) }+ (2) * {(1* -2)-(2 *-4) }

    =+ (-2) * {(2-6)} - (3) * {(1-12}+ (2) * {(-2+8) }
    =8 +33+12= 53
    Answer: 53

    20. Solve the system of equations by using Cramer's Rule.

    The system of equation is solved using the Cramer's rule

    det is the determinant
    D= det | 2 5 |
    | 5 7 |
    =2*7-5*5=-11

    D1= det | 9 5 |
    | 8 7 |
    =9*7-5*8= 23

    D2= det | 2 9 |
    | 5 8 |
    =2*8-5*9= -29

    x=D1/D= 23/(-11)= - 23/11
    y= D2/D= -29/(-11)= 29 /11

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com October 2, 2022, 2:30 pm ad1c9bdddf>
    https://brainmass.com/math/matrices/solve-system-equations-gaussian-elimination-method-5111

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