# Questions tagged [vector-spaces]

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

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### Linear Algebra Subspaces problem, MIT

Im trying to figure out how to arrive to the solution for problem number 8 below, Using the method of Problem 6, show that the set $\{a + (a + b)t^2 | a, b ∈ \mathbb R\}$ is a subspace of $P_2$. ...
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### Discriminant of a matrix with respect to change of basis

According to "Commutative Ring Theory" by Matsumura:" If $A$ is a finite $k$-algebra, the trace of an element $\alpha$ of $A$ denoted by $tr_{A/k}(\alpha)$ is the trace of the $k$-...
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### Critique my understanding of the determinant's relation to linear independence

If $det(A) = 0$ then the columns of $A$ are linearly dependent. This is a result that I could recite but struggled to reconcile after having completed my first course in elementary linear algebra. ...
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