Which one of the followings is equal to  ⎛⎝⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜00000100⎞⎠⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟(00000100)  ?

To determine which of the given options is equal to the matrix represented by

$\begin{pmatrix} 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ \end{pmatrix}$

let's break down the analysis.

1. ### Understanding the Matrix

The matrix provided appears to be a single row matrix (a row vector). Specifically, it's a 1x8 matrix consisting of seven zeros followed by a one in the sixth position.

2. ### Interpretation of the Matrix

The matrix can be interpreted as a representation of a standard basis vector in a more abstract sense or can also be thought of as a digital representation where the '1' indicates an active or true state, and the '0's represent inactive or false states.

3. ### Possible Equivalents

To find an equivalent expression, we would look for:

• Another row vector of the same dimension (1x8) with '1' in the sixth position and '0's elsewhere.
• Any mathematical notation that holds the same value or representation as the given matrix.

4. ### Summary of Findings

In essence, we are trying to identify any expressions or vectors that correctly represent the same state as the given matrix.

Without additional options to choose from, it's essential to understand that the equivalent representation must maintain the same dimension and configuration.

Final Answer

The matrix

$\begin{pmatrix} 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ \end{pmatrix}$

is equal to any row vector that has the same structure: that is, '1' in the sixth place and '0's elsewhere. If options were provided, one would compare them against this structure.