The rank and the nullity of A, respectively are [1 2 1 2 1 0 1 1 2 1 A 13 24 2 02242 0 0 0 0 0 "The Rank = "The Nullity= "
The rank and the nullity of A, respectively are [1 2 1 2 1 0 1 1 2 1 A 13 24 2 02242 0 0 0 0 0 "The Rank = "The Nullity= "
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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![**The rank and the nullity of A, respectively, are:**
\[ A = \begin{bmatrix}
1 & 2 & 1 & 2 & 1 \\
0 & 1 & 1 & 2 & 1 \\
1 & 3 & 2 & 4 & 2 \\
0 & 2 & 2 & 4 & 2 \\
0 & 0 & 0 & 0 & 0
\end{bmatrix} \]
The Rank = [ ]
The Nullity = [ ]
In this example, the matrix \(A\) is a 5x5 matrix. The rank of a matrix is the dimension of the column space (or the row space) of the matrix, and the nullity is the dimension of the null space of the matrix.
To calculate the rank:
1. Transform the matrix into its row echelon form (REF) or reduced row echelon form (RREF).
2. Count the number of non-zero rows to determine the rank.
For the nullity:
1. Subtract the rank from the number of columns of the matrix since Nullity = Number of columns - Rank.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5483afab-7850-40f6-959f-e698dea1419a%2F8b0da5d6-4ddf-47df-a977-494e6ab4cdfe%2Ftjxyw3x_processed.png&w=3840&q=75)
Transcribed Image Text:**The rank and the nullity of A, respectively, are:**
\[ A = \begin{bmatrix}
1 & 2 & 1 & 2 & 1 \\
0 & 1 & 1 & 2 & 1 \\
1 & 3 & 2 & 4 & 2 \\
0 & 2 & 2 & 4 & 2 \\
0 & 0 & 0 & 0 & 0
\end{bmatrix} \]
The Rank = [ ]
The Nullity = [ ]
In this example, the matrix \(A\) is a 5x5 matrix. The rank of a matrix is the dimension of the column space (or the row space) of the matrix, and the nullity is the dimension of the null space of the matrix.
To calculate the rank:
1. Transform the matrix into its row echelon form (REF) or reduced row echelon form (RREF).
2. Count the number of non-zero rows to determine the rank.
For the nullity:
1. Subtract the rank from the number of columns of the matrix since Nullity = Number of columns - Rank.
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