Exercise 2-1 - Gauss-Jordan Elimination PDF

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MATH 3499 – Differential Equations and Linear Systems for Mechanical Engineers Exercise 2-1 Topics: Gauss-Jordan elimination

1. Solve the following systems of equations using the method of Gauss-Jordan elimination.  x + 3y = 4 a.  2x − y = 1 6x − 4 y = 2 b.  4x + 8y = 8  2 x − y = 17 c.  4x − 8 = 2 y

 2 x + 4 y + 6z = 4  d.  x + 5 y + 9z = 2  2 x + y + 3z = 7   x + y −z =2  e.  x − 3 y + 2z = 1  3x − 5y + 3z = 4 

f.

 2x + y + z = 4   x − 2y − z = 3  3x + 3y − 2z = 1 

 4x − 16y + 2z = − 50  g.  −3 x +12 y + 2 z = 48  −2 x + 8 y + 4 z = 40   2x + 4 y − z = 2  h.  −6 x −12 y + 3 z = −6  8 x +16 y − 4 z = 8 

i.

 3x + 4y − z = − 9   4x + 3y + 2z = 0  − x − 6 y + 7 z = 19 

MATH 3499 – Differential Equations and Linear Systems for Mechanical Engineers 2. Solve the following systems of equations using the method of Gauss-Jordan elimination.

 −3 x + 4 y − 12 z = −66  a.  −3 x + 6 y −18 z = −102  2 x − 2 y + 4 z = 22   2x + y + z = 4  b.  x − 2 y − z = 3  3x + 3y − 2z = 1   i1 + i2 + i3 = 0  c.  6i1 − 10i3 = 8  6i − 2i = 5 2  1

3. Solve the following systems of equations using the method of Gauss-Jordan elimination.

 −4 x − 9 y −10 z = −36  a.  3 x + 9 y +12 z = 45  −2 x − 2 y − z = −4   2x + y + 1= 0  b.  3x − 2y + 5 = 0  x −4 y +5 = 0  5 3 1 x− y =  c.  2 + 1 = 7  x y

 x = y − 2z  d.  2 y = x + 3z + 1 z = 2 y − 2x − 3 

MATH 3499 – Differential Equations and Linear Systems for Mechanical Engineers  1 1 1  x+ y+z =5  2 3 4 e.  − − = − 11 x y z  3 2 1  x + y − z = −6 

f.

 2x + 4y + 6z = 4   x + 5 y + 9z = 2  2 x + y + 3z = 7 

 2 x − 3 y + 3z = 7  g.  3x + y − 2z = − 11  5x − 2y + 4z = 11   3a + 2 b − 4 c + 2 d = 3  5a − 3b − 5c + 6d = 8  h.   2a − b + 3c − 2d = 1  −2 a + 3b + 2 c − 3d = −2

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