# Tagged Questions

For questions about vector spaces and their properties. More general questions about linear algebra belong under the [tag:linear-algebra] tag. A vector space is a space which consists of elements called "vectors", which can be added and multiplied by scalars. In other words, these are the spaces ...

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### Dimension of a subspace smaller than dimension of intersection

Suppose I have a finite-dimensional vector space $V$, and $U_1, U_2$ are subspaces of $V$, such that $U_1\nsubseteq U_2$. Is it possible that $\dim{U_1}\leq\dim{U_1 \cap U_2}$?
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### How to convert from cartesian to vector form (of a straight line)

line in question: $$-x - 1 = \frac 12y - \frac12 = \frac 12z + 1$$ I wasn't really sure how to go about this one since it's not in the exact general form that I was taught, but I went along and ...
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### What are the objects and morphisms of the category $\operatorname{Vect}$?

What are the objects and morphisms of the category $\operatorname{Vect}$? I am trying to learn category theory, and it seems we have infinite objects in $\operatorname{Vect}$ being all of the finite ...
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### Why the column space of a matrix is useful?

I know what is the column space of a matrix: it is basically the subspace formed by the linear combinations of the columns (vectors) of a matrix. From wikipedia, we have the following nice picture: ...
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### How to find if this huge vector is in the column space of this huge matrix?

I newbie to linear algebra, so I hope you are patient with me. I have to say if a vector $\vec{u} = \left[ \begin{matrix} 1 \\ 1 \\ 1 \\ 0 \\ 0 \\ 1 \\ 1\end{matrix} \right]$ is in the column space ...