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seen Dec 1 at 20:39

May
28
comment If two planes in $\mathbb{R}^3$ pass by the origin, do they necessarily intersect at multiple points?
@user3001408: Nice, my entire life was a lie.
May
28
accepted If two planes in $\mathbb{R}^3$ pass by the origin, do they necessarily intersect at multiple points?
May
28
asked If two planes in $\mathbb{R}^3$ pass by the origin, do they necessarily intersect at multiple points?
May
28
accepted Calculating a basis in $\mathbb{R}^4$.
May
28
asked Calculating a basis in $\mathbb{R}^4$.
May
28
comment Calculating a basis given some constraints.
@David: When I multiplied by $s$, the third term should've been $1$, not the fourth. Ack....... By the way, for this specific method, my basis should always be identical to the solution in the book, right? Or can they differ?
May
28
asked Calculating a basis given some constraints.
May
28
accepted Does linear dependency have anything to do when determining a span?
May
28
comment Does linear dependency have anything to do when determining a span?
Thanks! Yeah I couldn't find the right word. What would you have said?
May
28
comment Does linear dependency have anything to do when determining a span?
Ok so, the dimension of $\mathbb{R}^2$ is 2, therefore its basis must have $2$ vectors. Since a basis contains the minimum number of vectors needed to span $\mathbb{R}^2$, any set of vectors that supposedly span $\mathbb{R}^2$ must have, as a minimum, 2 vectors. Then $\{(1,1),(2,2)\}$ can't be a span because it has only one significant vector, whereas it needs at least 2, right? So a set of 3 vectors can span $\mathbb{R}^2$, as long as two of its vectors are linearly independent, yes?
May
28
asked Does linear dependency have anything to do when determining a span?
May
27
asked Proving that a subset is a subspace by showing a scalar combination.
May
27
accepted When proving if a subset is a subspace, can I prove closure under addition and multiplication in a single proof?
May
27
comment When proving if a subset is a subspace, can I prove closure under addition and multiplication in a single proof?
Reckon this would apply to any problem of this kind, or only certain ones?
May
27
asked When proving if a subset is a subspace, can I prove closure under addition and multiplication in a single proof?
May
27
accepted Proving $||\vec{a}+\vec{b}|| = ||\vec{a}-\vec{b}|| \iff \vec{a} \perp \vec{b}$
May
27
asked Proving $||\vec{a}+\vec{b}|| = ||\vec{a}-\vec{b}|| \iff \vec{a} \perp \vec{b}$
May
27
accepted If $n$ vectors are linearly independent, is their span $\mathbb{R}^n$?
May
26
comment If $n$ vectors are linearly independent, is their span $\mathbb{R}^n$?
@Muphrid: My concept of Span is pretty basic. To me, it's just the set of all vectors resulting from all linear combinations of the $n$ vectors.
May
26
asked If $n$ vectors are linearly independent, is their span $\mathbb{R}^n$?