Short Answer

Determine whether the statements that follow are true or false, and justify your answer.
17: Rank $| \begin{matrix} 2 & 2 & 2 \\ 2 & 2 & 2 \\ 2 & 2 & 2 \end{matrix} | = 2$

False, Rank of $|\begin{matrix} 2 & 2 & 2 \\ 2 & 2 & 2 \\ 2 & 2 & 2 \end{matrix}| = 1$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1:Rank of matrix

For finding the rank of matrix first of all we will change the given matrix in the echelon form.

We have given the matrix.

$|\begin{matrix} 2 & 2 & 2 \\ 2 & 2 & 2 \\ 2 & 2 & 2 \end{matrix}|$

Step 2: Justification of answer

Now, reduce the given matrix into row echelon form.

$|\begin{matrix} 2 & 2 & 2 \\ 2 & 2 & 2 \\ 2 & 2 & 2 \end{matrix}| R_{2} \to R_{2} - R_{1} R_{3} \to R_{3} - R_{1} ~ |\begin{matrix} 2 & 2 & 2 \\ 2 & 2 & 2 \\ 2 & 2 & 2 \end{matrix}|$

Now, the given matrix is in echelon form. Thus, the number of non-zero rows is equal to the rank of the matrix.

Thus, the rank of the given matrix is 1.

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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.
17: Rank $| \begin{matrix} 2 & 2 & 2 \\ 2 & 2 & 2 \\ 2 & 2 & 2 \end{matrix} | = 2$

Step by Step Solution

Step 1:Rank of matrix

Step 2: Justification of answer

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Linear Algebra With Applications

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Step by Step Solution

Step 1:Rank of matrix

Step 2: Justification of answer

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Determine whether the statements that follow are true or false, and justify your answer.
17: Rank $| \begin{matrix} 2 & 2 & 2 \\ 2 & 2 & 2 \\ 2 & 2 & 2 \end{matrix} | = 2$