In each of the following cases, compute a basis matrix for the null space of the matrix A and express the points x; as x; = Pi +qi where p; is in the null space of A and q; is in the range space of A'. -2) 4 A = (1 1 1 1), x1 = X2 = %3D -13 -2 1
In each of the following cases, compute a basis matrix for the null space of the matrix A and express the points x; as x; = Pi +qi where p; is in the null space of A and q; is in the range space of A'. -2) 4 A = (1 1 1 1), x1 = X2 = %3D -13 -2 1
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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![**Exercises**
**2.1** In each of the following cases, compute a basis matrix for the null space of the matrix \( A \) and express the points \( x_i \) as \( x_i = p_i + q_i \) where \( p_i \) is in the null space of \( A \) and \( q_i \) is in the range space of \( A^T \).
**(ii)**
\[
A = (1 \quad 1 \quad 1 \quad 1), \quad x_1 = \begin{pmatrix} -2 \\ 4 \\ 5 \\ -2 \end{pmatrix}, \quad x_2 = \begin{pmatrix} 7 \\ 5 \\ -13 \\ 1 \end{pmatrix}
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Transcribed Image Text:**Exercises**
**2.1** In each of the following cases, compute a basis matrix for the null space of the matrix \( A \) and express the points \( x_i \) as \( x_i = p_i + q_i \) where \( p_i \) is in the null space of \( A \) and \( q_i \) is in the range space of \( A^T \).
**(ii)**
\[
A = (1 \quad 1 \quad 1 \quad 1), \quad x_1 = \begin{pmatrix} -2 \\ 4 \\ 5 \\ -2 \end{pmatrix}, \quad x_2 = \begin{pmatrix} 7 \\ 5 \\ -13 \\ 1 \end{pmatrix}
\]
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