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The formula $\mathbf{W}_h = [\mathbf{W}_h^1 \mathbf{W}_h^2 ... \mathbf{W}_h^M]$ defines a matrix $\mathbf{W}_h$ that is formed by the horizontal concatenation of a sequence of matrices or vectors, from $\mathbf{W}_h^1$ to $\mathbf{W}_h^M$.

Concatenated Matrix Notation ($\mathbf{W}_h$)

Given the matrices **A** = [[1, 2], [3, 4]] and **B** = [[5, 6], [7, 8]], what is the resulting matrix **C** from the operation **C** = [**A** **B**]?

Consider the matrix $\mathbf{C}$ formed by the horizontal concatenation of $N$ matrices, $\mathbf{A}_1, \mathbf{A}_2, ..., \mathbf{A}_N$, represented as $\mathbf{C} = [\mathbf{A}_1 \mathbf{A}_2 ... \mathbf{A}_N]$. If each matrix $\mathbf{A}_i$ has dimensions $m \times n_i$, what are the dimensions of the resulting matrix $\mathbf{C}$? Explain the reasoning behind both the row and column dimensions of the final matrix.

Dimensionality of Concatenated Matrices

A matrix $\mathbf{W}$ is formed by horizontally combining two other matrices, $\mathbf{A}$ and $\mathbf{B}$, such that $\mathbf{W} = [\mathbf{A} \mathbf{B}]$. If $\mathbf{W}$ is given as [[1, 0, 5, 6], [2, 1, 7, 8]], which of the following options correctly identifies a possible pair for matrices $\mathbf{A}$ and $\mathbf{B}$?

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