At Westonci.ca, we provide reliable answers to your questions from a community of experts. Start exploring today! Join our Q&A platform and connect with professionals ready to provide precise answers to your questions in various areas. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
To solve the problem of performing the elementary row operation [tex]\( 5R_2 + R_1 \rightarrow R_1 \)[/tex] on the matrix
[tex]\[ \left[\begin{array}{ccc} 0 & -6 & 2 \\ 0 & -5 & 8 \end{array}\right] \][/tex]
we will follow a step-by-step approach.
### Step 1: Identify the Multiples
First, we need to determine the multiples of the elements of the second row [tex]\( R_2 \)[/tex].
[tex]\[ 5 \times R_2 = 5 \times \left[\begin{array}{ccc} 0 & -5 & 8 \end{array}\right] = \left[\begin{array}{ccc} 0 & -25 & 40 \end{array}\right] \][/tex]
### Step 2: Add the Result to the First Row
Next, we add the result from step 1 to the elements of the first row [tex]\( R_1 \)[/tex]:
[tex]\[ R_1 + 5R_2 = \left[\begin{array}{ccc} 0 & -6 & 2 \end{array}\right] + \left[\begin{array}{ccc} 0 & -25 & 40 \end{array}\right] = \left[\begin{array}{ccc} 0 & -31 & 42 \end{array}\right] \][/tex]
### Step 3: Replace the First Row with the Result
Finally, we replace the first row [tex]\( R_1 \)[/tex] with the result from step 2:
[tex]\[ \left[\begin{array}{ccc} 0 & -31 & 42 \\ 0 & -5 & 8 \end{array}\right] \][/tex]
### Final Matrix Configuration
The matrix after performing the elementary row operation [tex]\( 5R_2 + R_1 \rightarrow R_1 \)[/tex] is:
[tex]\[ \left[\begin{array}{ccc} 0 & -31 & 42 \\ 0 & -5 & 8 \end{array}\right] \][/tex]
Thus, the resulting rows are:
- [tex]\(R_1 = [0, -31, 42] \)[/tex]
- [tex]\(R_2 = [0, -5, 8]\)[/tex]
This is the final answer.
[tex]\[ \left[\begin{array}{ccc} 0 & -6 & 2 \\ 0 & -5 & 8 \end{array}\right] \][/tex]
we will follow a step-by-step approach.
### Step 1: Identify the Multiples
First, we need to determine the multiples of the elements of the second row [tex]\( R_2 \)[/tex].
[tex]\[ 5 \times R_2 = 5 \times \left[\begin{array}{ccc} 0 & -5 & 8 \end{array}\right] = \left[\begin{array}{ccc} 0 & -25 & 40 \end{array}\right] \][/tex]
### Step 2: Add the Result to the First Row
Next, we add the result from step 1 to the elements of the first row [tex]\( R_1 \)[/tex]:
[tex]\[ R_1 + 5R_2 = \left[\begin{array}{ccc} 0 & -6 & 2 \end{array}\right] + \left[\begin{array}{ccc} 0 & -25 & 40 \end{array}\right] = \left[\begin{array}{ccc} 0 & -31 & 42 \end{array}\right] \][/tex]
### Step 3: Replace the First Row with the Result
Finally, we replace the first row [tex]\( R_1 \)[/tex] with the result from step 2:
[tex]\[ \left[\begin{array}{ccc} 0 & -31 & 42 \\ 0 & -5 & 8 \end{array}\right] \][/tex]
### Final Matrix Configuration
The matrix after performing the elementary row operation [tex]\( 5R_2 + R_1 \rightarrow R_1 \)[/tex] is:
[tex]\[ \left[\begin{array}{ccc} 0 & -31 & 42 \\ 0 & -5 & 8 \end{array}\right] \][/tex]
Thus, the resulting rows are:
- [tex]\(R_1 = [0, -31, 42] \)[/tex]
- [tex]\(R_2 = [0, -5, 8]\)[/tex]
This is the final answer.
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.