Find the rank of the given matrix: 1 1 0 2 -234 4 68 1 00 568
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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Good afternoon,
Having some problems with rank of a matrix. Thanks!
![**Find the rank of the given matrix:**
\[
\begin{bmatrix}
1 & -2 & 3 & 4 \\
1 & 4 & 6 & 8 \\
0 & 1 & 0 & 0 \\
2 & 5 & 6 & 8
\end{bmatrix}
\]
**Explanation:**
This is a 4x4 matrix presented with four rows and four columns. The task is to determine the rank of the matrix, which is the maximum number of linearly independent row or column vectors in the matrix. The rank indicates the dimensionality of the vector space spanned by its rows or columns. To find the rank, you can use methods such as row reduction to echelon form or evaluating determinants of submatrices.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F89a69b77-6859-4c30-95b3-e6df6014c589%2Feb81d1cf-8919-4af1-b5b7-ae622dc65301%2Ffbbze8c_processed.png&w=3840&q=75)
Transcribed Image Text:**Find the rank of the given matrix:**
\[
\begin{bmatrix}
1 & -2 & 3 & 4 \\
1 & 4 & 6 & 8 \\
0 & 1 & 0 & 0 \\
2 & 5 & 6 & 8
\end{bmatrix}
\]
**Explanation:**
This is a 4x4 matrix presented with four rows and four columns. The task is to determine the rank of the matrix, which is the maximum number of linearly independent row or column vectors in the matrix. The rank indicates the dimensionality of the vector space spanned by its rows or columns. To find the rank, you can use methods such as row reduction to echelon form or evaluating determinants of submatrices.
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