Students frequently perform the following type of calculation to introduce a zero into a matrix. 31 3R₂-2R₁ 31 [24] 0 10 However, 3R₂ - 2R₁ is not an elementary row operation. Why not? O 3R₂ - 2R₁ is not an elementary row operation since the coefficient of R₂ is -2. 3R₂ - 2R₁ is not an elementary row operation since it does not include the interchanging of two rows. 3R₂ - 2R₁ is not an elementary row operation since the coefficient of R₂ is 3. 3R₂ - 2R₁ is not an elementary row operation since the coefficient of R₁₂ is 2. 3R₂ -2R₁ is not an elementary row operation since the coefficient of R₁ is -3. Show how to achieve the same result using elementary row operations. - First perform the elementary row operation R₂ -₁, R₁, then perform 2R₂. 3 Perform the elementary row operation R₂ - 3₁. O First perform the elementary row operation R₂ - 3 O Perform the elementary row operation R₂ - ³₁. 2 First perform the elementary row operation R₂ - 2R₁, then perform 3R2. ₁, then perform 3R₂.
Students frequently perform the following type of calculation to introduce a zero into a matrix. 31 3R₂-2R₁ 31 [24] 0 10 However, 3R₂ - 2R₁ is not an elementary row operation. Why not? O 3R₂ - 2R₁ is not an elementary row operation since the coefficient of R₂ is -2. 3R₂ - 2R₁ is not an elementary row operation since it does not include the interchanging of two rows. 3R₂ - 2R₁ is not an elementary row operation since the coefficient of R₂ is 3. 3R₂ - 2R₁ is not an elementary row operation since the coefficient of R₁₂ is 2. 3R₂ -2R₁ is not an elementary row operation since the coefficient of R₁ is -3. Show how to achieve the same result using elementary row operations. - First perform the elementary row operation R₂ -₁, R₁, then perform 2R₂. 3 Perform the elementary row operation R₂ - 3₁. O First perform the elementary row operation R₂ - 3 O Perform the elementary row operation R₂ - ³₁. 2 First perform the elementary row operation R₂ - 2R₁, then perform 3R2. ₁, then perform 3R₂.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![Students frequently perform the following type of calculation to introduce a zero into a matrix.
Given the matrix:
\[
\begin{bmatrix}
3 & 1 \\
2 & 4
\end{bmatrix}
\]
Apply the operation \(3R_2 - 2R_1\) to transform it into:
\[
\begin{bmatrix}
3 & 1 \\
0 & 10
\end{bmatrix}
\]
However, \(3R_2 - 2R_1\) is not an elementary row operation. Why not?
- \(3R_2 - 2R_1\) is not an elementary row operation since the coefficient of \(R_2\) is \(-2\).
- \(3R_2 - 2R_1\) is not an elementary row operation since it does not include the interchanging of two rows.
- \(3R_2 - 2R_1\) is not an elementary row operation since the coefficient of \(R_2\) is 3.
- \(3R_2 - 2R_1\) is not an elementary row operation since the coefficient of \(R_1\) is 2.
- \(3R_2 - 2R_1\) is not an elementary row operation since the coefficient of \(R_1\) is \(-3\).
Show how to achieve the same result using elementary row operations.
- First perform the elementary row operation \(R_2 - \frac{3}{2}R_1\), then perform \(2R_2\).
- Perform the elementary row operation \(R_2 - \frac{2}{3}R_1\).
- First perform the elementary row operation \(R_2 - \frac{2}{3}R_1\), then perform \(3R_2\).
- Perform the elementary row operation \(R_2 - \frac{3}{2}R_1\).
- First perform the elementary row operation \(R_2 - 2R_1\), then perform \(3R_2\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff8fa7aa4-dafc-4c07-b274-462aa6ff800c%2Ffa6e6e63-1dd9-4146-90ef-c54bea99b19c%2Ffju3gre_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Students frequently perform the following type of calculation to introduce a zero into a matrix.
Given the matrix:
\[
\begin{bmatrix}
3 & 1 \\
2 & 4
\end{bmatrix}
\]
Apply the operation \(3R_2 - 2R_1\) to transform it into:
\[
\begin{bmatrix}
3 & 1 \\
0 & 10
\end{bmatrix}
\]
However, \(3R_2 - 2R_1\) is not an elementary row operation. Why not?
- \(3R_2 - 2R_1\) is not an elementary row operation since the coefficient of \(R_2\) is \(-2\).
- \(3R_2 - 2R_1\) is not an elementary row operation since it does not include the interchanging of two rows.
- \(3R_2 - 2R_1\) is not an elementary row operation since the coefficient of \(R_2\) is 3.
- \(3R_2 - 2R_1\) is not an elementary row operation since the coefficient of \(R_1\) is 2.
- \(3R_2 - 2R_1\) is not an elementary row operation since the coefficient of \(R_1\) is \(-3\).
Show how to achieve the same result using elementary row operations.
- First perform the elementary row operation \(R_2 - \frac{3}{2}R_1\), then perform \(2R_2\).
- Perform the elementary row operation \(R_2 - \frac{2}{3}R_1\).
- First perform the elementary row operation \(R_2 - \frac{2}{3}R_1\), then perform \(3R_2\).
- Perform the elementary row operation \(R_2 - \frac{3}{2}R_1\).
- First perform the elementary row operation \(R_2 - 2R_1\), then perform \(3R_2\).
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