Problem 16. Construct a matrix with the required property or say why that it is impossible. 1 2 (a) Column space contains | 2 and -3, and nullspace contains 1 -3 부산 5 1 2 and -3, and nullspace contains 5 (b) Row space contains | 2 1 (c) Ax = 1 has a solution and AT 0 [] 0 I 0 0
Problem 16. Construct a matrix with the required property or say why that it is impossible. 1 2 (a) Column space contains | 2 and -3, and nullspace contains 1 -3 부산 5 1 2 and -3, and nullspace contains 5 (b) Row space contains | 2 1 (c) Ax = 1 has a solution and AT 0 [] 0 I 0 0
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 16.** Construct a matrix with the required property or say why it is impossible.
(a) Column space contains
\[
\begin{bmatrix} 1 \\ 2 \\ -3 \end{bmatrix}
\]
and
\[
\begin{bmatrix} 2 \\ -3 \\ 5 \end{bmatrix}
\],
and nullspace contains
\[
\begin{bmatrix} 1 \\ 1 \end{bmatrix}
\].
(b) Row space contains
\[
\begin{bmatrix} 1 & 2 & -3 \end{bmatrix}
\]
and
\[
\begin{bmatrix} 2 & -3 & 5 \end{bmatrix}
\],
and nullspace contains
\[
\begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix}
\].
(c) \( Ax = \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix} \) has a solution and
\[
A^T \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix}
\].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff009717e-378a-40e4-98f6-43d73e41bae3%2Fb94d78a7-4884-4d3e-8e2e-ef0f0587d1e6%2F6n7ij8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 16.** Construct a matrix with the required property or say why it is impossible.
(a) Column space contains
\[
\begin{bmatrix} 1 \\ 2 \\ -3 \end{bmatrix}
\]
and
\[
\begin{bmatrix} 2 \\ -3 \\ 5 \end{bmatrix}
\],
and nullspace contains
\[
\begin{bmatrix} 1 \\ 1 \end{bmatrix}
\].
(b) Row space contains
\[
\begin{bmatrix} 1 & 2 & -3 \end{bmatrix}
\]
and
\[
\begin{bmatrix} 2 & -3 & 5 \end{bmatrix}
\],
and nullspace contains
\[
\begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix}
\].
(c) \( Ax = \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix} \) has a solution and
\[
A^T \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix}
\].
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