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# Equations and Matrices

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

#### Solution Preview

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 ...

#### Solution Summary

Solves system of equations by the Gaussian elimination method, find the inverse of the given matrix, evaluates the determinant by expanding by cofactors and solves the system of equations by using Cramer's Rule.

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