459 results for "linear".

Question in Content created by Newcastle University
Real numbers $a,\;b,\;c$ and $d$ are such that $a+b+c+d=1$ and for the given vectors $\textbf{v}_1,\;\textbf{v}_2,\;\textbf{v}_3,\;\textbf{v}_4$ $a\textbf{v}_1+b\textbf{v}_2+c\textbf{v}_3+d\textbf{v}_4=\textbf{0}$. Find $a,\;b,\;c,\;d$.

Question in Content created by Newcastle University
Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

Question in Content created by Newcastle University
Student is given a set of constraints for a linear program. Asked to enter the constraints as inequalities, and then to identify the optimal solution.
Problem with solving the simultaneous equations gven by the constraints  too unwieldy and not given enough marks for doing so. Best if the point of intersection is given graphically by putting the mouse over the intersection.

Question in Content created by Newcastle University
Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix.

Question in Content created by Newcastle University
Given three linear combinations of four i.i.d. variables, find the expectation and variance of these estimators of the mean $\mu$. Which are unbiased and efficient?

Exam (15 questions) in Content created by Newcastle UniversityQuestions used in a university course titled "Linear algebra"

Exam (2 questions) in Content created by Newcastle University
Solve a linear programming problem, and perform sensitivity analysis.

Question in Content created by Newcastle University
Let $P_n$ denote the vector space over the reals of polynomials $p(x)$ of degree $n$ with coefficients in the real numbers. Let the linear map $\phi: P_4 \rightarrow P_4$ be defined by: \[\phi(p(x))=p(a)+p(bx+c).\]Using the standard basis for range and domain find the matrix given by $\phi$.

Question in Content created by Newcastle University
Let $P_n$ denote the vector space over the reals of polynomials $p(x)$ of degree $n$ with coefficients in the real numbers.
Let the linear map $\phi: P_4 \rightarrow P_4$ be defined by:
$\phi(p(x))=ap(x) + (bx + c)p'(x) + (x ^ 2 + dx + f)p''(x)$
Using the standard basis for range and domain find the matrix given by $\phi$.

Question in Content created by Newcastle University
Student is shown a linear programming problem, with graphical solution.
Asked to identify binding constraints, and decide if the optimal solution is changed by a named constraint either doubling or halving.

Question in Content created by Newcastle University
Factorise $x^2+bx+c$ into 2 distinct linear factors and then find $\displaystyle \int \frac{a}{x^2+bx+c }\;dx$ using partial fractions or otherwise.

Question in Content created by Newcastle University
Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Question in Content created by Newcastle University
Solve for $x$: $\displaystyle ax+b = cx+d$

Question in Content created by Newcastle University
Given a linear programming problem in standard form, write down the dual problem.

Question in Content created by Newcastle University
Given a linear programming problem in standard form, write down the dual problem.

Question in Content created by Newcastle University
The derivative of $\displaystyle \frac{ax+b}{cx^2+dx+f}$ is $\displaystyle \frac{g(x)}{(cx^2+dx+f)^2}$. Find $g(x)$.

Question in Content created by Newcastle University
The derivative of $\displaystyle \frac{ax+b}{\sqrt{cx+d}}$ is $\displaystyle \frac{g(x)}{2(cx+d)^{3/2}}$. Find $g(x)$.

Question in Content created by Newcastle University
Other method. Find $p,\;q$ such that $\displaystyle \frac{ax+b}{cx+d}= p+ \frac{q}{cx+d}$. Find the derivative of $\displaystyle \frac{ax+b}{cx+d}$.

Exam (2 questions) in Content created by Newcastle University
Given linear programming problems in standard form, write down the dual problem.

Question in Content created by Newcastle University
Finding the value of a variable

Question in Content created by Newcastle University
Factorise $\displaystyle{ax ^ 2 + bx + c}$ into linear factors.

Question in Content created by Newcastle University
Dividing a cubic polynomial by a linear polynomial. Find quotient and remainder.

Question in Content created by Newcastle University
Solving simple linear equations in $\mathbb{Q}$ and $\mathbb{Z}_n$ for $n= 13, \;17$ or $19$.

Question in Content created by Newcastle University
Expanding products of 3 linear polynomials over $\mathbb{Z}_3,\;\mathbb{Z}_5,\;\mathbb{Z}_7$

Question in Transition to university
Apply the factor theorem to check which of a list of linear polynomials are factors of another polynomial.

Question in Transition to university
Describe a given linear transformation as a vector in Cartesian coordinates.

Question in Transition to university
Solve a linear equation of the form $ax+b = c$, where $a$, $b$ and $c$ are integers.
The answer is always an integer.

Question in Transition to university
In the first three parts, rearrange linear inequalities to make $x$ the subject.
In the last four parts, correctly give the direction of the inequality sign after rearranging an inequality.

Question in Transition to university
This question tests the student's ability to solve simple linear equations by elimination. Part a) involves only having to manipulate one equation in order to solve, and part b) involves having to manipulate both equations in order to solve.

Question in Transition to university
Solve a simple linear equation algebraically. The unknown appears on both sides of the equation.