Chapter 4: Q7. (page 192)

Use Cramer’s Rule to solve each system of equations.
$2 x - y + 3 z = 5$
$3 x + 2 y - 5 z = 4$
$x - 4 y + 11 z = 3$

Short Answer

Expert verified

The system of equation has no solutions.

Step by step solution

Step 1- Determine the value of x

Apply the Cramer’s rule for the value of x.

$x = \frac{|\begin{matrix} j & b & c \\ k & e & f \\ l & h & i \end{matrix}|}{|\begin{matrix} a & b & c \\ d & e & f \\ g & h & i \end{matrix}|}$

Use the provided equations and substitute the value of a, b, c, d, e, f, g, h, i, j, k and l into role="math" localid="1647355463064" $x = \frac{|\begin{matrix} j & b & c \\ k & e & f \\ l & h & i \end{matrix}|}{|\begin{matrix} a & b & c \\ d & e & f \\ g & h & i \end{matrix}|}$ after it perform simplification of determinants to write the value of x.

$\begin{matrix} x = \frac{|\begin{matrix} 5 & - 1 & 3 \\ 4 & 2 & - 5 \\ 3 & - 4 & 11 \end{matrix}|}{|\begin{matrix} 2 & - 1 & 3 \\ 3 & 2 & - 5 \\ 1 & - 4 & 11 \end{matrix}|} \\ = \frac{3}{0} \end{matrix}$

– Analyze the obtained value of x

The denominator of the value of x is 0 which means that the main determinant is 0 so each value will become undefined.

Step 3- Make the conclusion

The obtained value of each value is undefined which means that there is no solution of the given system of equations.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Use Cramer’s Rule to solve each system of equations.
$2 x - y + 3 z = 5$
$3 x + 2 y - 5 z = 4$
$x - 4 y + 11 z = 3$

Short Answer

Step by step solution

Step 1- Determine the value of x

– Analyze the obtained value of x

Step 3- Make the conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Geometry

Calculus

Discrete Mathematics

Decision Maths

Statistics

Study anywhere. Anytime. Across all devices.

Use Cramer’s Rule to solve each system of equations.2x-y+3z=53x+2y-5z=4x-4y+11z=3

Short Answer

Step by step solution

Step 1- Determine the value of x

– Analyze the obtained value of x

Step 3- Make the conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Geometry

Calculus

Discrete Mathematics

Decision Maths

Statistics

Study anywhere. Anytime. Across all devices.

Use Cramer’s Rule to solve each system of equations.
$2 x - y + 3 z = 5$
$3 x + 2 y - 5 z = 4$
$x - 4 y + 11 z = 3$