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3 years ago

Solve the system of equations using matrices. Use the Gaussian elimination method with back-substitution.

Mathematics

1 answer:

Naddika [18.5K]3 years ago

7 0

Answer:

Step-by-step explanation:

Ⅰ. x+y-z = -3

Ⅱ. 4x-y+z = 8

Ⅲ. -x+5y-4z = 1

Use equation Ⅰ to eliminate the x terms from equations Ⅱ and Ⅲ.

Ⅰ. x+y-z = -3

Ⅱ. -5y+5z = 20

Ⅲ. 6y-5z = -2

Divide equation Ⅱ by the coefficient of its y term:

Ⅰ. x+y-z = -3

Ⅱ. y-z = -4

Ⅲ. 6y-5z = -2

Use equation Ⅱ to eliminate the y terms from equation Ⅲ.

Ⅰ. x+y-z = -3

Ⅱ. y-z = -4

Ⅲ. z = 22

Divide equation Ⅲ by the coefficient of its z term:

Ⅰ. x+y-z = -3

Ⅱ. y-z = -4

Ⅲ. z = 22

Back-substitution

y = -4 - (-1)z = 18

x = -3 - (1)y - (-1)z = 1

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Nutka1998 [239]

Answer:

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Step-by-step explanation:

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Solve the system of equations using matrices. Use the Gaussian elimination method with​ back-substitution.

Solve the system of equations using matrices. Use the Gaussian elimination method with back-substitution.