Give the rank and nullity of the matrix below. 4 -8 0 4 1 -1 2 1 4 8 3-6 18 9 A = rank(A) = nullity (A) =
Give the rank and nullity of the matrix below. 4 -8 0 4 1 -1 2 1 4 8 3-6 18 9 A = rank(A) = nullity (A) =
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
![**Matrix Rank and Nullity Exercise**
Determine the rank and nullity of the given matrix.
Matrix \( A \):
\[
A = \begin{bmatrix}
4 & -8 & 0 & 4 & 1 \\
-1 & 2 & 1 & 4 & 8 \\
3 & -6 & 1 & 8 & 9
\end{bmatrix}
\]
**Rank of Matrix \( A \):**
rank(\( A \)) = [ ]
**Nullity of Matrix \( A \):**
nullity(\( A \)) = [ ]
In this exercise, you are asked to find the rank and nullity of the matrix \( A \). The rank of a matrix is the dimension of the column space (or the row space), which corresponds to the number of linearly independent columns (or rows). The nullity is the dimension of the null space, which corresponds to the number of linearly independent solutions to the homogeneous equation \( A\mathbf{x} = \mathbf{0} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff6948d5d-782c-4f32-af22-abf47b4c3397%2F0011e7e9-74ed-4089-9c46-3f49564bbd3e%2Fq4nzsso_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Matrix Rank and Nullity Exercise**
Determine the rank and nullity of the given matrix.
Matrix \( A \):
\[
A = \begin{bmatrix}
4 & -8 & 0 & 4 & 1 \\
-1 & 2 & 1 & 4 & 8 \\
3 & -6 & 1 & 8 & 9
\end{bmatrix}
\]
**Rank of Matrix \( A \):**
rank(\( A \)) = [ ]
**Nullity of Matrix \( A \):**
nullity(\( A \)) = [ ]
In this exercise, you are asked to find the rank and nullity of the matrix \( A \). The rank of a matrix is the dimension of the column space (or the row space), which corresponds to the number of linearly independent columns (or rows). The nullity is the dimension of the null space, which corresponds to the number of linearly independent solutions to the homogeneous equation \( A\mathbf{x} = \mathbf{0} \).
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