Chapter 11: Q. 17 (page 729)

Write the system of equations corresponding to each augmented matrix. Then perform the indicated row operation(s) on the given augmented matrix.
$[\begin{matrix} 1 & - 3 | & - 2 \\ 2 & - 5 | & 5 \end{matrix}], R_{2} = - 2 r_{1} + r_{2}$

Short Answer

Expert verified

The resultant matrix is

$[\begin{matrix} 1 & - 3 | & - 2 \\ 0 & 1 | & 9 \end{matrix}]$

Step by step solution

Step 1. Given Information

The given matrix and operation is

$[\begin{matrix} 1 & - 3 | & - 2 \\ 2 & - 5 | & 5 \end{matrix}], R_{2} = - 2 r_{1} + r_{2}$

Step 2. Explanation

The given matrix has two rows. So, it represents a system of two linear equations. The 2 columns to the left of vertical bar indicate that the system has two variables.

Let the variables be x and y. Then system of linear equation corresponding to the given matrix is as follows,

$x - 3 y = - 2 - - - (1) 2 x - 5 y = 5 - - - (2)$

Apply the given row operation on the given augmented matrix and then simplify

role="math" localid="1647334029961" $[\begin{matrix} 1 & - 3 | & - 2 \\ 2 & - 5 | & 5 \end{matrix}] \to [\begin{matrix} 1 & - 3 | & - 2 \\ - 2 (1) + 2 & - 2 (- 3) + (- 5) | & - 2 (- 2) + 5 \end{matrix}] \to [\begin{matrix} 1 & - 3 | & - 2 \\ 0 & 1 | & 9 \end{matrix}]$

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.

Write the system of equations corresponding to each augmented matrix. Then perform the indicated row operation(s) on the given augmented matrix.
$[\begin{matrix} 1 & - 3 | & - 2 \\ 2 & - 5 | & 5 \end{matrix}], R_{2} = - 2 r_{1} + r_{2}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Discrete Mathematics

Geometry

Mechanics Maths

Logic and Functions

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Write the system of equations corresponding to each augmented matrix. Then perform the indicated row operation(s) on the given augmented matrix.1-3|-22-5|5,R2=-2r1+r2

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Discrete Mathematics

Geometry

Mechanics Maths

Logic and Functions

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Write the system of equations corresponding to each augmented matrix. Then perform the indicated row operation(s) on the given augmented matrix.
$[\begin{matrix} 1 & - 3 | & - 2 \\ 2 & - 5 | & 5 \end{matrix}], R_{2} = - 2 r_{1} + r_{2}$