Finite spanning set of a polynomialQuestion concerning sum of spanning setsLinear algebra, polynomial problemLet $P$ be the set of all polynomials of degree $leq 3$ such that $p(t) = t$. Is $P$ a subspace of $P_3$?Determine whether the vector is a spanning set, dependent set, and if it has a basis.Finite dimensional subspace of a finite dimensional vector spaceIs there any trigonometric function that cannot be written as an infinite series?finding inner productThe set of real sequences has no countable spanning setExplicitly finding a quotient of two polynomial spacesSpanning set definition and theorem
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Finite spanning set of a polynomial
Question concerning sum of spanning setsLinear algebra, polynomial problemLet $P$ be the set of all polynomials of degree $leq 3$ such that $p(t) = t$. Is $P$ a subspace of $P_3$?Determine whether the vector is a spanning set, dependent set, and if it has a basis.Finite dimensional subspace of a finite dimensional vector spaceIs there any trigonometric function that cannot be written as an infinite series?finding inner productThe set of real sequences has no countable spanning setExplicitly finding a quotient of two polynomial spacesSpanning set definition and theorem
$begingroup$
I am currently looking at a set of polynomials that looks like this:
$$S = p_0 + p_1x + p_2x^2 + p_3x^3 in P_3 $$
$$ V = p_3$$
V is a vector space and S represents a subspace of V.
How can I go about determining the finite spanning set of this? I'm been re-reading my textbook for over an hour and I am just so confused!
linear-algebra polynomials
edited Mar 21 at 18:28
David G. Stork
11.9k41735
asked Mar 21 at 18:16
larnlarn
12
$endgroup$
|
show 2 more comments
$begingroup$
I am currently looking at a set of polynomials that looks like this:
$$S = p_0 + p_1x + p_2x^2 + p_3x^3 in P_3 $$
$$ V = p_3$$
V is a vector space and S represents a subspace of V.
How can I go about determining the finite spanning set of this? I'm been re-reading my textbook for over an hour and I am just so confused!
linear-algebra polynomials
edited Mar 21 at 18:28
David G. Stork
11.9k41735
asked Mar 21 at 18:16
larnlarn
12
$endgroup$
$begingroup$
Welcome to the website. Look here for a tutorial on Mathjax.
$endgroup$
– Shubham Johri
Mar 21 at 18:21
$begingroup$
what is $V$? is that some vector space?
$endgroup$
– Jneven
Mar 21 at 18:22
$begingroup$
@Jneven Probably polynomials with real coefficients and degree $3$ or less, i.e. $P_3(x)$.
$endgroup$
– Shubham Johri
Mar 21 at 18:23
$begingroup$
@Jneven V is a vector space and S (the set of polynomials) is a subspace of V.
$endgroup$
– larn
Mar 21 at 18:24
$begingroup$
@iam so you should write this in the question as this are important details
$endgroup$
– Jneven
Mar 21 at 18:24
|
show 2 more comments
$begingroup$
I am currently looking at a set of polynomials that looks like this:
$$S = p_0 + p_1x + p_2x^2 + p_3x^3 in P_3 $$
$$ V = p_3$$
V is a vector space and S represents a subspace of V.
How can I go about determining the finite spanning set of this? I'm been re-reading my textbook for over an hour and I am just so confused!
linear-algebra polynomials
edited Mar 21 at 18:28
David G. Stork
11.9k41735
asked Mar 21 at 18:16
larnlarn
12
$endgroup$
I am currently looking at a set of polynomials that looks like this:
$$S = p_0 + p_1x + p_2x^2 + p_3x^3 in P_3 $$
$$ V = p_3$$
V is a vector space and S represents a subspace of V.
How can I go about determining the finite spanning set of this? I'm been re-reading my textbook for over an hour and I am just so confused!
linear-algebra polynomials
linear-algebra polynomials
edited Mar 21 at 18:28
David G. Stork
11.9k41735
asked Mar 21 at 18:16
larnlarn
12
edited Mar 21 at 18:28
David G. Stork
11.9k41735
asked Mar 21 at 18:16
larnlarn
12
edited Mar 21 at 18:28
David G. Stork
11.9k41735
edited Mar 21 at 18:28
David G. Stork
11.9k41735
edited Mar 21 at 18:28
David G. Stork
11.9k41735
11.9k41735
asked Mar 21 at 18:16
larnlarn
12
asked Mar 21 at 18:16
larnlarn
12
asked Mar 21 at 18:16
larnlarn
12
12
$begingroup$
Welcome to the website. Look here for a tutorial on Mathjax.
$endgroup$
– Shubham Johri
Mar 21 at 18:21
$begingroup$
what is $V$? is that some vector space?
$endgroup$
– Jneven
Mar 21 at 18:22
$begingroup$
@Jneven Probably polynomials with real coefficients and degree $3$ or less, i.e. $P_3(x)$.
$endgroup$
– Shubham Johri
Mar 21 at 18:23
$begingroup$
@Jneven V is a vector space and S (the set of polynomials) is a subspace of V.
$endgroup$
– larn
Mar 21 at 18:24
$begingroup$
@iam so you should write this in the question as this are important details
$endgroup$
– Jneven
Mar 21 at 18:24
|
show 2 more comments
$begingroup$
Welcome to the website. Look here for a tutorial on Mathjax.
$endgroup$
– Shubham Johri
Mar 21 at 18:21
$begingroup$
what is $V$? is that some vector space?
$endgroup$
– Jneven
Mar 21 at 18:22
$begingroup$
@Jneven Probably polynomials with real coefficients and degree $3$ or less, i.e. $P_3(x)$.
$endgroup$
– Shubham Johri
Mar 21 at 18:23
$begingroup$
@Jneven V is a vector space and S (the set of polynomials) is a subspace of V.
$endgroup$
– larn
Mar 21 at 18:24
$begingroup$
@iam so you should write this in the question as this are important details
$endgroup$
– Jneven
Mar 21 at 18:24
$begingroup$
Welcome to the website. Look here for a tutorial on Mathjax.
$endgroup$
– Shubham Johri
Mar 21 at 18:21
$begingroup$
Welcome to the website. Look here for a tutorial on Mathjax.
$endgroup$
– Shubham Johri
Mar 21 at 18:21
$begingroup$
what is $V$? is that some vector space?
$endgroup$
– Jneven
Mar 21 at 18:22
$begingroup$
what is $V$? is that some vector space?
$endgroup$
– Jneven
Mar 21 at 18:22
$begingroup$
@Jneven Probably polynomials with real coefficients and degree $3$ or less, i.e. $P_3(x)$.
$endgroup$
– Shubham Johri
Mar 21 at 18:23
$begingroup$
@Jneven Probably polynomials with real coefficients and degree $3$ or less, i.e. $P_3(x)$.
$endgroup$
– Shubham Johri
Mar 21 at 18:23
$begingroup$
@Jneven V is a vector space and S (the set of polynomials) is a subspace of V.
$endgroup$
– larn
Mar 21 at 18:24
$begingroup$
@Jneven V is a vector space and S (the set of polynomials) is a subspace of V.
$endgroup$
– larn
Mar 21 at 18:24
$begingroup$
@iam so you should write this in the question as this are important details
$endgroup$
– Jneven
Mar 21 at 18:24
$begingroup$
@iam so you should write this in the question as this are important details
$endgroup$
– Jneven
Mar 21 at 18:24
|
show 2 more comments
1 Answer
1
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$begingroup$
$p_0=p_1=5p_3implies p_0+p_1x+p_2x^2+p_3x^3=p_0(1+x+dfracx^35)+p_2x^2$. Thus, $S$ is spanned by the vectors $1+x+dfracx^35,x^2$.
answered Mar 21 at 18:27
Shubham JohriShubham Johri
5,500818
$endgroup$
add a comment |
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$begingroup$
$p_0=p_1=5p_3implies p_0+p_1x+p_2x^2+p_3x^3=p_0(1+x+dfracx^35)+p_2x^2$. Thus, $S$ is spanned by the vectors $1+x+dfracx^35,x^2$.
answered Mar 21 at 18:27
Shubham JohriShubham Johri
5,500818
$endgroup$
add a comment |
$begingroup$
$p_0=p_1=5p_3implies p_0+p_1x+p_2x^2+p_3x^3=p_0(1+x+dfracx^35)+p_2x^2$. Thus, $S$ is spanned by the vectors $1+x+dfracx^35,x^2$.
answered Mar 21 at 18:27
Shubham JohriShubham Johri
5,500818
$endgroup$
add a comment |
$begingroup$
$p_0=p_1=5p_3implies p_0+p_1x+p_2x^2+p_3x^3=p_0(1+x+dfracx^35)+p_2x^2$. Thus, $S$ is spanned by the vectors $1+x+dfracx^35,x^2$.
answered Mar 21 at 18:27
Shubham JohriShubham Johri
5,500818
$endgroup$
$p_0=p_1=5p_3implies p_0+p_1x+p_2x^2+p_3x^3=p_0(1+x+dfracx^35)+p_2x^2$. Thus, $S$ is spanned by the vectors $1+x+dfracx^35,x^2$.
answered Mar 21 at 18:27
Shubham JohriShubham Johri
5,500818
answered Mar 21 at 18:27
Shubham JohriShubham Johri
5,500818
answered Mar 21 at 18:27
Shubham JohriShubham Johri
5,500818
answered Mar 21 at 18:27
Shubham JohriShubham Johri
5,500818
5,500818
add a comment |
add a comment |
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$begingroup$
Welcome to the website. Look here for a tutorial on Mathjax.
$endgroup$
– Shubham Johri
Mar 21 at 18:21
$begingroup$
what is $V$? is that some vector space?
$endgroup$
– Jneven
Mar 21 at 18:22
$begingroup$
@Jneven Probably polynomials with real coefficients and degree $3$ or less, i.e. $P_3(x)$.
$endgroup$
– Shubham Johri
Mar 21 at 18:23
$begingroup$
@Jneven V is a vector space and S (the set of polynomials) is a subspace of V.
$endgroup$
– larn
Mar 21 at 18:24
$begingroup$
@iam so you should write this in the question as this are important details
$endgroup$
– Jneven
Mar 21 at 18:24