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Consider the following system -4x-20y-85z = 1 3x+19y+83z = 4 6x+30y+126z = 2Solve...

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swimmers | Student | (Level 2) Honors

Posted April 26, 2013 at 2:37 PM via web

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Consider the following system

-4x-20y-85z = 1

3x+19y+83z = 4

6x+30y+126z = 2

Solve for x using Cramer's Rule.
det(A_1) = ? and x = ?

Solve for y using Cramer's Rule.
det(A_2) = ?? and y = ??

Solve for z using Cramer's Rule.
det(A_3) = ?? and z = ???

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted April 26, 2013 at 3:42 PM (Answer #1)

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You need to use Cramer's rule to determine x,y,z, such that:

`x = (det A_1)/(det A), y = (detA_2)/(det A), z = (det A_3)/(det A)`

You need to determine `det A` , such that:

`det A = [(-4,-20,-85),(3,19,83),(6,30,126)]`

`det A = -9576 - 7650 - 9960 + 9690 + 9960 + 7560`

`det A = 24`

You need to replace the first column by the column of constant terms to evaluate `det A_1` , such that:

`det A_1 = [(1,-20,-85),(4,19,83),(2,30,126)]`

`det A_1 = 2394 - 10200 - 3320 + 3230 - 2490 + 10080`

`det A_1 = -306`

`x = -306/24 => x = -12.75`

`det A_2 = [(-4,1,-85),(3,4,83),(6,2,126)]`

`det A_2 = -2016 - 510 + 498 + 2040 + 664 - 378`

`det A_2 = -298 => y = -298/24 => y = -149/12`

`det A_3 = [(-4,-20,1),(3,19,4),(6,30,2)]`

`det A_3 = -152 + 90 - 480 - 114 + 480 + 120`

`det A_3 = -56 => z = -56/24 => z = -7/3`

Hence, evaluating the solution to the system of equations, using Cramer's rule, yields `x = -12.75, y = -149/12, z = -7/3.`

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bogshow24 | Student | (Level 2) Honors

Posted April 26, 2013 at 7:39 PM (Answer #2)

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You need to use Cramer's rule to determine x,y,z, such that:

You need to determine , such that:

You need to replace the first column by the column of constant terms to evaluate , such that:

Hence, evaluating the solution to the system of equations, using Cramer's rule, yields

This answer is correct except the -298 should be 298 ad the -149/12 should be 149/12

 

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