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Use Cramer’s rule to solve for x: x + 4y − z = −14 5x + 6y + 3z = 4 −2x + 7y + 2z = −17
A=
AX=
A= -240, -120, 120, 240.
AX= -240, -120, 120, 240.
X=

Respuesta :

Ashraf82

Answer:

A = -120

AX = -240

X = 2

Step-by-step explanation:

∵ x + 4y - z = -14

∵ 5x + 6y + 3z = 4

∵ -2x + 7y + 2z = -17

[tex]\left[\begin{array}{ccc}1&4&-1\\5&6&3\\-2&7&2\end{array}\right]=\left[\begin{array}{ccc}-14\\4\\-17\end{array}\right][/tex]

∴ A = 1(6×2 - 3×7) + (-4)(2×5 - 3×-2) + (-1)(5×7 - 6×-2)

∴ A = 1(12 - 21) + (-4)(10 - -6) + (-1)(35 - -12)

∴ A = -9 + (-4)(16) + (-1)(47) = -9 - 64 - 47 = -120

To find X replace the column of X by the column of the answer

[tex]\left[\begin{array}{ccc}-14&4&-1\\4&6&3\\-17&7&2\end{array}\right][/tex]

∴ AX = -14(6×2 - 3×7) + (-4)(4×2 - 3×-17) + (-1)(4×7 - 6×-17)

∴ AX = -14(12 - 21) + (-4)(8 - -51) + (-1)(28 - -102)

∴ AX = 126 + (-4)(59) + (-1)(130) = 126 - 236 - 130 = -240

∴ X = AX/A = -240/-120 = 2

From the given three equations, we have;

  • A = -120
  • AX = -240
  • X = 2

How can Cramer's rule be used to find X?

The given linear systems of equations are presented as follows;

x + 4•y - z = -14

5•x + 6•y + 3•z = 4

-2•x + 7•y + 2•z = -17

Which gives;

  • A = 1×(6×2-3×7) + 4×((5×2) - 3×(-2)) + (-1)×(5×7-6×(-2)) = -120

AX is found as follows;

Substituting the first row, with the right side of the equation, we have;

-14 + 4•y - z

4 + 6•y + 3•z

-17 + 7•y + 2•z

  • AX = -14×(6×2-3×7) + 4×((4×2) - 3×(-17)) + (-1)×(4×7-6×(-17)) = -240

X = AX/A

Which gives;

X = -240/(-120) = 2

Learn more about linear systems of equations here:

https://brainly.com/question/11637584

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