Given the matrix 3 -3 -6 3 0 -2 2 5-4-2 Use elementary row operations to carry it to a matrix that is a) In row-echelon form: Г0 0 0 0 Row-echelon form: 0 000 0000
Given the matrix 3 -3 -6 3 0 -2 2 5-4-2 Use elementary row operations to carry it to a matrix that is a) In row-echelon form: Г0 0 0 0 Row-echelon form: 0 000 0000
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![**Given Matrix:**
\[
\left[\begin{array}{ccccc}
3 & -3 & -6 & 3 & 0 \\
-2 & 2 & 5 & -4 & -2
\end{array}\right]
\]
Use elementary row operations to convert it to a matrix that is:
**a) In row-echelon form:**
\[
\left[\begin{array}{ccccc}
0 & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 0
\end{array}\right]
\]
**Explanation:**
The initial matrix is a 2x5 matrix:
\[
\left[\begin{array}{ccccc}
3 & -3 & -6 & 3 & 0 \\
-2 & 2 & 5 & -4 & -2
\end{array}\right]
\]
To perform elementary row operations means to use techniques such as row swapping, row addition, and multiplying rows by scalar values to transform the matrix into row-echelon form (a form where all non-zero rows are above rows of all zeros, and the leading entry of each non-zero row after the first occurs to the right of the leading entry of the previous row).
In this case, the row-echelon form provided in the problem is a zero matrix, which indicates that both rows have been manipulated (likely through a series of row operations) to become zero rows:
\[
\left[\begin{array}{ccccc}
0 & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 0
\end{array}\right]
\]
This transformation reflects that all the original entries of the matrix have been nullified through the row operations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd936c6c0-8e3b-4a92-9646-2c460fec57ae%2F4a74a880-f3f9-48b0-85b2-09e2c10305a2%2Fiznmgdc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Given Matrix:**
\[
\left[\begin{array}{ccccc}
3 & -3 & -6 & 3 & 0 \\
-2 & 2 & 5 & -4 & -2
\end{array}\right]
\]
Use elementary row operations to convert it to a matrix that is:
**a) In row-echelon form:**
\[
\left[\begin{array}{ccccc}
0 & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 0
\end{array}\right]
\]
**Explanation:**
The initial matrix is a 2x5 matrix:
\[
\left[\begin{array}{ccccc}
3 & -3 & -6 & 3 & 0 \\
-2 & 2 & 5 & -4 & -2
\end{array}\right]
\]
To perform elementary row operations means to use techniques such as row swapping, row addition, and multiplying rows by scalar values to transform the matrix into row-echelon form (a form where all non-zero rows are above rows of all zeros, and the leading entry of each non-zero row after the first occurs to the right of the leading entry of the previous row).
In this case, the row-echelon form provided in the problem is a zero matrix, which indicates that both rows have been manipulated (likely through a series of row operations) to become zero rows:
\[
\left[\begin{array}{ccccc}
0 & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 0
\end{array}\right]
\]
This transformation reflects that all the original entries of the matrix have been nullified through the row operations.
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