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1 0 1 Find a basis for the null space of the matrix A = 0 0 0 9 0 9

1 0 1 Find a basis for the null space of the matrix A = 0 0 0 9 0 9

Advanced Engineering Mathematics
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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**Problem Statement:** Find a basis for the null space of the matrix \( A = \begin{bmatrix} 1 & 0 & 1 \\ 0 & 0 & 0 \\ 9 & 0 & 9 \end{bmatrix} \). **Explanation:** This problem requires identifying the null space of matrix \( A \), which consists of all vectors \( x \) such that \( A \cdot x = 0 \). A basis for this null space is a set of linearly independent vectors that span this space. The matrix \( A \) has three rows and three columns and notably includes a row of zeros, which is indicative of dependent equations in a system or automatically extends the null space. Solving this would typically involve setting up and solving the system of linear equations represented by the matrix equation \( A \cdot x = 0 \).
Transcribed Image Text:**Problem Statement:** Find a basis for the null space of the matrix \( A = \begin{bmatrix} 1 & 0 & 1 \\ 0 & 0 & 0 \\ 9 & 0 & 9 \end{bmatrix} \). **Explanation:** This problem requires identifying the null space of matrix \( A \), which consists of all vectors \( x \) such that \( A \cdot x = 0 \). A basis for this null space is a set of linearly independent vectors that span this space. The matrix \( A \) has three rows and three columns and notably includes a row of zeros, which is indicative of dependent equations in a system or automatically extends the null space. Solving this would typically involve setting up and solving the system of linear equations represented by the matrix equation \( A \cdot x = 0 \).
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