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By default, vectors are visualized as column vectors, where their elements are stacked vertically. In formal mathematical notation, a vector $$\mathbf{x}$$ with elements $$x_1, \ldots, x_n$$ is represented as a column matrix enclosed in brackets:
$$ \mathbf{x} = \begin{bmatrix} x_{1} \\ \vdots \\ x_{n} \end{bmatrix} $$
This is in contrast to row vectors, whose elements are stacked horizontally.

Column Vector Representation

Consider a vector defined by the ordered components (12, -7). The formal mathematical representation of this vector as a column matrix is `[12  -7]`.

A two-dimensional vector is defined by the components 5 (for the first dimension) and -3 (for the second dimension). Write the formal representation of this vector as a column matrix.

Vector to Column Matrix Representation

A vector is defined by the ordered components (5, -1, 9). Which of the following correctly represents this vector as a column matrix using formal mathematical notation?

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