Chapter 11: Q. 13 (page 795)

solve each system of equations using matrices.
If the system has no solution, say that it is inconsistent.
$6 x + 3 y = 12 2 x - y = - 2$

Short Answer

Expert verified

The solution to the equation is $(\frac{1}{2}, 3)$ .

Step by step solution

Step 1. Given

$6 x + 3 y = 12 2 x - y = - 2$

Step 2. Augmented matrix

$6 x + 3 y = 12 2 x - y = - 2 C o n s i d e r, 6 x + 3 y = 12 2 x + y = 4 t h e r e f o r e t h e a u g m e n t e d m a t r i x w i l l b e [\begin{matrix} 2 & 1 & 4 \\ 2 & - 1 & - 2 \end{matrix}]$

Step 3. Calculation using transformation

$[\begin{matrix} 2 & 1 & 4 \\ 2 & - 1 & - 2 \end{matrix}] R_{1} = \frac{r_{1}}{2} [\begin{matrix} 2 & 1 & 4 \\ 2 & - 1 & - 2 \end{matrix}] \to [\begin{matrix} 1 & \frac{1}{2} & 2 \\ 2 & - 1 & - 2 \end{matrix}] N o w R_{2} = r_{2} - 2 r_{1} [\begin{matrix} 1 & \frac{1}{2} & 2 \\ 2 & - 1 & - 2 \end{matrix}] \to [\begin{matrix} 1 & \frac{1}{2} & 2 \\ 0 & - 2 & - 6 \end{matrix}] N o w R_{2} = \frac{r_{2}}{- 2} [\begin{matrix} 1 & \frac{1}{2} & 2 \\ 0 & - 2 & - 6 \end{matrix}] \to [\begin{matrix} 1 & \frac{1}{2} & 2 \\ 0 & 1 & 3 \end{matrix}] t h u s w e g e t x + \frac{1}{2} y = 3 y = 3 t h e r e f o r e (x, y) = (\frac{1}{2}, 3)$

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.

solve each system of equations using matrices.
If the system has no solution, say that it is inconsistent.
$6 x + 3 y = 12 2 x - y = - 2$

Short Answer

Step by step solution

Step 1. Given

Step 2. Augmented matrix

Step 3. Calculation using transformation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Calculus

Geometry

Mechanics Maths

Pure Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

solve each system of equations using matrices.If the system has no solution, say that it is inconsistent.6x+3y=122x-y=-2

Short Answer

Step by step solution

Step 1. Given

Step 2. Augmented matrix

Step 3. Calculation using transformation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Calculus

Geometry

Mechanics Maths

Pure Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

solve each system of equations using matrices.
If the system has no solution, say that it is inconsistent.
$6 x + 3 y = 12 2 x - y = - 2$