598 results authored by Newcastle University Mathematics and Statistics  search across all users.

Question in Content created by Newcastle University
Curl and divergence of a vector field. Determine whether the vector field is irrotational or solenoidal.

Question in Content created by Newcastle University
Multiplication and addition of complex numbers. Four parts.

Question in Content created by Newcastle University
Adding linear combinations of polynomials over $\mathbb{Z}_3,\;\mathbb{Z}_5,\;\mathbb{Z}_7$

Question in Content created by Newcastle University
Correct an error in a received message which was encoded using Hamming's square code

Question in Content created by Newcastle University
Decode a message of two codewords encoded using Hamming's [7,4] code, with at most one error per codeword.

Question in Content created by Newcastle University
Compute the information rate and minimum distance of some binary codes.

Question in Content created by Newcastle University
Find upper and lower bounds on the number of codewords in three maximal codes given their codeword lengths and minimum distances.
Uses Hamming, Singleton and GilbertVarshamov bounds.

Question in Content created by Newcastle University
List all vectors in a spanning set.
(repeated 3 times)

Question in Content created by Newcastle University
Write down a lexicographic parity check matrix for a Hamming code and correct two received codewords.

Question in Content created by Newcastle University
Write down the lexicographic parity check matrix for a Hamming code, and correct two received codewords.

Question in Content created by Newcastle University
Compute the word length, minimum distance and dimension of some given Hamming codes.

Question in Content created by Newcastle University
Parametric form of a curve, cartesian points, tangent vector, and speed.

Question in Content created by Newcastle University
A plane goes through three given noncollinear points in 3space. Find the Cartesian equation of the plane in the form $ax+by+cz=d$.
There is a problem in that this equation can be multiplied by a constant and be correct. Perhaps d can be given as this makes a,b and c unique and the method of the question will give the correct solution.

Question in Content created by Newcastle University
Calculation of the length and alternative form of the parameteric representation of a curve, involving trigonometric functions.

Question in Content created by Newcastle University
Find the Cartesian form $ax+by+cz=d$ of the equation of the plane $\boldsymbol{r=r_0+\lambda a+\mu b}$.
The solution is not unique. The constant on right hand side could be given to ensure that the left hand side is unique.

Question in Content created by Newcastle University
Determine if various combinations of vectors are defined or not.

Question in Content created by Newcastle University
When are vectors $\boldsymbol{v,\;w}$ orthogonal?
Part b) is not answered in Advice, the given solution is for a different question.

Question in Content created by Newcastle University
Find minimum distance between a point and a line in 3space. The line goes through a given point in the direction of a given vector.
The correct solution is given, however the accuracy of 0.001 is not enough as in some cases answers near to the correct solution are also marked as correct.

Question in Content created by Newcastle University
Given vectors $\boldsymbol{v,\;w}$, find the angle between them.

Question in Content created by Newcastle University
Find angle between plane $\Pi_1$, given by three points, and the plane $\Pi_2$ given in Cartesian form.
The calculation of $cos(\alpha)$ at the end of Advice has fractionNumbers switched on and so the result is presented as a fraction, which can be misleading. Best if calculation is followed through without using fractionNumbers.

Question in Content created by Newcastle University
Calculations of the lengths of two 3D vectors, the distance between their terminal points, their sum, difference, and dot and cross products.

Question in Content created by Newcastle University
Given vectors $\boldsymbol{v}$ and $\boldsymbol{w}$, find their inner product.

Question in Content created by Newcastle University
(Green’s theorem). $\Gamma$ a rectangle, find: $\displaystyle \oint_{\Gamma} \left(ax^2by \right)\;dx+\left(cy^2+px\right)\;dy$.

Question in Content created by Newcastle University
Find all words with given Hamming distance from a given codeword.

Question in Content created by Newcastle University
Compute tables of Hamming distances in given codes, then determine which codes are equivalent.

Question in Content created by Newcastle University
Given vectors $\boldsymbol{A,\;B}$, find $\boldsymbol{A\times B}$

Question in Content created by Newcastle University
Given a set of vectors, find a basis which generates their span as a subspace of $\mathbb{Z}_n$.

Question in Content created by Newcastle University
Given a pair of 3D position vectors, find the vector equation of the line through both. Find two such lines and their point of intersection.

Exam (11 questions) in Content created by Newcastle University
Questions on vector arithmetic and vector operations, including dot and cross product, as well as the vector equations of planes and lines.

Question in Content created by Newcastle University
Given a matrix in the field $\mathbb{Z}_n$. By reducing it to rowechelon form (or otherwise), find a basis for the row space of the matrix, as a list of vectors.