Book edition 5th

Author(s) Otto Bretscher

Pages 442 pages

ISBN 9780321796974

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Short Answer

Determine whether the statements that follow are true or false, and justify your answer.

15: The system $A \vec{x} = [\begin{matrix} 0 \\ 0 \\ 0 \\ 1 \end{matrix}]$ inconsistent for all $4 \times 3$ matrices A.

True, the given system of equations is inconsistent.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1:Corresponding augmented matrix

We have given that,a system of equationslets the A matrix be

$[\begin{matrix} a & e & i \\ b & f & j \\ c & g & k \\ d & h & l \end{matrix}]$

Now, we have given the system.

$A \vec{x} = [\begin{matrix} 0 \\ 0 \\ 0 \\ 1 \end{matrix}]$

Step 2: Justification of answer

Put the value of A matrix in the above equation we will get.

$[\begin{matrix} a & e & i \\ b & f & j \\ c & g & k \\ d & h & l \end{matrix}] \vec{x} = [\begin{matrix} 0 \\ 0 \\ 0 \\ 1 \end{matrix}]$

Now since the matrix A has 3 columns then it has a maximum of 3 pivot entry.

Also, the pivot entry not possible in the last row.

This means for any value of $\vec{x}$ the value $0 \neq 1$

Hence, the given statement is true, because the given system is inconsistent.

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Linear Algebra With Applications

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Short Answer

Determine whether the statements that follow are true or false, and justify your answer.

15: The system $A \vec{x} = [\begin{matrix} 0 \\ 0 \\ 0 \\ 1 \end{matrix}]$ inconsistent for all $4 \times 3$ matrices A.

Step by Step Solution

Step 1:Corresponding augmented matrix

Step 2: Justification of answer

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Linear Algebra With Applications

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Short Answer

Determine whether the statements that follow are true or false, and justify your answer. 15: The system Ax→=[0001]inconsistent for all 4×3matrices A.

Step by Step Solution

Step 1:Corresponding augmented matrix

Step 2: Justification of answer

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Determine whether the statements that follow are true or false, and justify your answer.

15: The system $A \vec{x} = [\begin{matrix} 0 \\ 0 \\ 0 \\ 1 \end{matrix}]$ inconsistent for all $4 \times 3$ matrices A.