Q. 394 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. 394 (page 483)

In the following exercise, solve the system of equations using Cramer鈥檚 rule
$\{\begin{cases} x + y - 3 z = - 1 \\ y - z = 0 \\ - x + 2 y = 1 \end{cases}$

Short Answer

Expert verified

This system of equations has infinitely many solutions.

Step by step solution

Step 1. Given information

The given system of equations is:

$\{\begin{cases} x + y - 3 z = - 1 \\ y - z = 0 \\ - x + 2 y = 1 \end{cases}$

Step 2. Evaluating the determinant D

In determinant $D$ all the coefficients are taken.

So,

$D = |\begin{matrix} 1 & 1 & - 3 \\ 0 & 1 & - 1 \\ - 1 & 2 & 0 \end{matrix}| D = 1 (0 + 2) - 1 (0 - 1) - 3 (0 + 1) D = 2 + 1 - 3 D = 0$

Step 3. Evaluating the determinant Dx

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

So,

$D_{x} = |\begin{matrix} - 1 & 1 & - 3 \\ 0 & 1 & - 1 \\ 1 & 2 & 0 \end{matrix}| D_{x} = - 1 (0 + 2) - 1 (0 + 1) - 3 (0 - 1) D_{x} = - 2 - 1 + 3 D_{x} = 0$

Step 4. Evaluating the determinant Dy

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

So,

$D_{y} = |\begin{matrix} 1 & - 1 & - 3 \\ 0 & 0 & - 1 \\ - 1 & 1 & 0 \end{matrix}| D_{y} = 1 (0 + 1) + 1 (0 - 1) - 3 (0 + 0) D_{y} = 1 - 1 D_{y} = 0$

Step 5. Evaluating the determinant Dz

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

So,

$D_{z} = |\begin{matrix} 1 & 1 & - 1 \\ 0 & 1 & 0 \\ - 1 & 2 & 1 \end{matrix}| D_{z} = 1 (1 - 0) - (0 - 0) - 1 (0 + 1) D_{z} = 0$

We can see that and $D_{z}$ are zero. So the system of equations is consistent and has infinitely many solutions.

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91影视

In the following exercise, solve the system of equations using Cramer鈥檚 rule
$\{\begin{cases} x + y - 3 z = - 1 \\ y - z = 0 \\ - x + 2 y = 1 \end{cases}$

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

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In the following exercise, solve the system of equations using Cramer鈥檚 rulex+y-3z=-1y-z=0-x+2y=1

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

One App. One Place for Learning.

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In the following exercise, solve the system of equations using Cramer鈥檚 rule
$\{\begin{cases} x + y - 3 z = - 1 \\ y - z = 0 \\ - x + 2 y = 1 \end{cases}$