Another question! V is a vector space in R4. And U={x=[x1,x2,x3,x4]: x1-2x2-3x3+x4=0}
so I'm happy this is a sunspace but I have to determine a basis and dimension.
Am I correct thinking that clearly there are non zero scalars such that x1+...+x4 equals zero, namely 1,-2,-3,1. So they are...
Ok right so the zero vector would be in U right? Just the one with all zero coefficients?
And the condition for p(0) - p'(0) = 0 is that p_{0}=p_{1} so provided you chose polynomials P and Q that satisfied this then (ap+bq)-(ap+bq)' = ap+bq-ap'-bq' = ap-ap' + bq-bq' = a(p-p')+b(q-q') = a0 +...
Homework Statement
For each of the following subsets U of the vector space V decide whether or not U is a
subspace of V . Give reasons for your answers. In each case when U is a subspace, find a
basis for U and state dim U
Homework Equations
V=P_{3} ; U=\left\{p\in\...
Homework Statement
Show that the following equation is continuous using the epsilon-delta definition at y=-2
Homework Equations
\f(y)=\sqrt[3]{y+3}
The Attempt at a Solution
so i got to a stage where...
Homework Statement
Compute \frac{d}{dx}\left(\frac{x^{n}\left(x-1\right)^{n}}{n!} \times e^{x}\right)
Homework Equations
\left(\frac{x^{n}\left(x-1\right)^{n}}{n!} \times e^{x}\right)
The Attempt at a Solution
I got a solution of sorts applying the product rule and then applying...
Homework Statement
In analogy with differential equations, the difference equation
x_{k}=x_{k-1}+x_{k-2}
has two solutions x_{k}=\beta^{k} for some \beta\neq0. Determine the two possible values of \beta.
Homework Equations
x_{k}=x_{k-1}+x_{k-2}
x_{k}=\beta^{k}
\beta\neq0
The...
Thanks i felt as though i new what i was doing but hours without sleep had caused me to doubt myself. Thanks for the concise reply and for the peace of mind.
Homework Statement
The function f is defined as f(x)=x^4, then;
f'(3x^3)=?
d[f(3x^3)]/dx=?
f'(xy^3)=?
Homework Equations
The Attempt at a Solution
My problem here is not so much doing the differentiation itself but understanding the notation.
1. for f'(3x^3) i want...