Q. 395 In the following exercise, solve... [FREE SOLUTION]

91影视

Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 4: Q. 395 (page 483)

In the following exercise, solve the system of equations using Cramer鈥檚 rule
$\{\begin{cases} 3 x + 4 y - 3 z = - 2 \\ 2 x + 3 y - z = - 12 \\ x + y - 2 z = 6 \end{cases}$

Short Answer

Expert verified

The given system of equations has no solution.

Step by step solution

Step 1. Given information

The given system of equations is:

$\{\begin{cases} 3 x + 4 y - 3 z = - 2 \\ 2 x + 3 y - z = - 12 \\ x + y - 2 z = 6 \end{cases}$

Step 2. Evaluating the determinant D

In determinant $D$ all the coefficients are taken.

So,

$D = |\begin{array}{llr} 3 & 4 & - 3 \\ 2 & 3 & - 1 \\ 1 & 1 & - 2 \end{array}| D = 3 (- 6 + 1) - 4 (- 4 + 1) - 3 (2 - 3) D = - 15 + 12 + 3 D = 0$

Step 3. Evaluating the determinant Dx

In the determinant $D_{x}$ , we take the constant in place of coefficients of

So,

$D_{x} = |\begin{matrix} - 2 & 4 & - 3 \\ - 12 & 3 & - 1 \\ 6 & 1 & - 2 \end{matrix}| D_{x} = 3 (24 + 6) + 2 (- 4 + 1) - 3 (12 + 12) D_{x} = 90 - 6 - 72 D_{x} = 12$

Step 4. Evaluating the determinant Dy

In the determinant $D_{y}$ , we take the constant in place of coefficients of

So,

role="math" localid="1644602420099" $D_{y} = |\begin{matrix} 3 & - 2 & - 3 \\ 2 & - 12 & - 1 \\ 1 & 6 & - 2 \end{matrix}| D_{y} = 3 (24 + 6) + 2 (- 4 + 1) - 3 (12 + 12) D_{y} = 90 - 6 - 72 D_{y} = 12$

Step 5. Evaluating the determinant Dz

In the determinant $D_{z}$ , we take the constant in place of coefficients of

So,

$D_{z} = |\begin{matrix} 3 & 4 & - 2 \\ 2 & 3 & - 12 \\ 1 & 1 & 6 \end{matrix}| D_{z} = 3 (18 + 12) - 4 (12 + 12) - 2 (2 - 3) D_{z} = 90 - 96 + 2 D_{z} = - 4$

Step 6. finding solution

We can see that $D = 0$ and $D_{x}, D_{y}$ and $D_{z}$ is not equal to zero. So the system is inconsistent and has no solution.

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91影视

In the following exercise, solve the system of equations using Cramer鈥檚 rule
$\{\begin{cases} 3 x + 4 y - 3 z = - 2 \\ 2 x + 3 y - z = - 12 \\ x + y - 2 z = 6 \end{cases}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Evaluating the determinant D

Step 3. Evaluating the determinant Dx

Step 4. Evaluating the determinant Dy

Step 5. Evaluating the determinant Dz

Step 6. finding solution

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91影视

In the following exercise, solve the system of equations using Cramer鈥檚 rule3x+4y-3z=-22x+3y-z=-12x+y-2z=6

Short Answer

Step by step solution

Step 1. Given information

Step 2. Evaluating the determinant D

Step 3. Evaluating the determinant Dx

Step 4. Evaluating the determinant Dy

Step 5. Evaluating the determinant Dz

Step 6. finding solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

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Pure Maths

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Applied Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercise, solve the system of equations using Cramer鈥檚 rule
$\{\begin{cases} 3 x + 4 y - 3 z = - 2 \\ 2 x + 3 y - z = - 12 \\ x + y - 2 z = 6 \end{cases}$