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Papers (30)
2025
pgmath 18
2024
pgmath 4 ugmath 20
2023
pgmath 12 ugmath 16
2022
pgmath 18 ugmath_22may 16 ugmath_23may 16
2021
pgmath 11 ugmath 15
2020
pgmath 18 ugmath 16
2019
pgmath 20 ugmath 15
2018
pgmath 4 ugmath 6
2017
ugmath 15
2016
pgmath 10 ugmath 16
2015
pgmath 5 ugmath 13
2014
ugmath 9
2013
pgmath 11 ugmath 12
2012
pgmath 24 ugmath 14
2011
pgmath 15 ugmath 12
2010
pgmath 4 ugmath 19
2010 pgmath

4 maths questions

QA4 Matrices True/False or Multiple-Select Conceptual Reasoning View
There exists a real $3 \times 3$ orthogonal matrix with only non-zero entries.
QA5 Invariant lines and eigenvalues and vectors True/false or multiple-choice on spectral properties View
A $5 \times 5$ real matrix has an eigenvector in $\mathbb{R}^5$.
QB4 Matrices Linear Transformation and Endomorphism Properties View
A linear transformation $T : \mathbb{R}^8 \rightarrow \mathbb{R}^8$ is defined on the standard basis $e_1, \ldots, e_8$ by $$\begin{aligned} & T e_j = e_{j+1} \quad j = 1, \ldots, 5 \\ & T e_6 = e_7 \\ & T e_7 = e_6 \\ & T e_8 = e_2 + e_4 + e_6 + e_8. \end{aligned}$$ What is the nullity of $T$?
QB9 Number Theory Prime Number Properties and Identification View
Let $f(x) = x^n + a_{n-1} x^{n-1} + \cdots + a_0$ be a polynomial with integer coefficients and whose degree is at least 2. Suppose each $a_i$ ($0 \leq i \leq n-1$) is of the form $$a_i = \pm \frac{17!}{r!(17-r)!}$$ with $1 \leq r \leq 16$. Show that $f(m)$ is not equal to zero for any integer $m$.