454 results for "linear".

Question in NC Math 4
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Exam (15 questions) in NC Math 4Plot linear functions and identify key characteristics.

Question in Demos
Customised for the Numbas demo exam
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.
Video in Show steps.

Question in PV EnglishFormulate a recurrence relation (= difference equation) and solve this recurrence relation.

Question in Linear Programming
Given a linear programming problem in standard form, write down the dual problem.

Question in PH023 Foundation Mathematics for Physicists 1
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Question in PH023 Foundation Mathematics for Physicists 1
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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
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
Given a generating matrix for a binary linear code, construct a parity check matrix, list all the codewords, list all the words in a given coset, give coset leaders, calculate syndromes for each coset, correct a codeword with one error.

Question in Content created by Newcastle University
Given a generating matrix for a linear code, give a parity check matrix

Question in Content created by Newcastle University
Given a generator matrix for a linear code, write a parity check matrix, compute the syndrome of a word, and decide if it's a codeword.

Question in Content created by Newcastle University
Three 3 dim vectors, one with a parameter $\lambda$ in the third coordinate. Find value of $\lambda$ ensuring vectors coplanar. Scalar triple product.

Question in Content created by Newcastle University
A multiple linear regression model of the form:
\[Y=\beta_0+\beta_1X_1+ \beta_2X_2+\beta_3X_3+\beta_4X_4+\epsilon \]
is fitted to some data in Minitab which generates a table showing estimates of the parameters with associated $p$values. Determine which variable to exclude first.

Exam (1 question) in Content created by Newcastle University
Solve a system of linear equations using Gaussian elimination.

Exam (2 questions) in Content created by Newcastle University
Use the simplex method to solve a linear program.

Question in Content created by Newcastle University
Linear program described in words. Student must write out constraints as equations in standard form, then identify the optimal solution in a finished simplex tableau.

Question in Content created by Newcastle University
Given a linear combination $Y$ of three independent random variables with given means and variances, find the mean of variance of $Y$.

Question in Content created by Newcastle University
Find a regression equation.

Question in Content created by Newcastle University
Approximating integral of a linear function by Riemann sums . Includes an interactive graph in Advice showing the approximations given by the upper and lower sums and how they vary as we increase the number of intervals.

Question in Content created by Newcastle University
Approximating integral of a linear function by Riemann sums . Includes an interactive graph in Advice showing the approximations given by the upper and lower sums and how they vary as we increase the number of intervals.

Question in Content created by Newcastle University
Find a regression equation.

Question in Content created by Newcastle University
Moving averages, regression and seasonal adjustments.

Question in Content created by Newcastle University
Given the following three vectors $\textbf{v}_1,\;\textbf{v}_2,\;\textbf{v}_3$ Find out whether they are a linearly independent set are not. Also if linearly dependent find the relationship $\textbf{v}_{r}=p\textbf{v}_{s}+q\textbf{v}_{t}$ for suitable $r,\;s,\;t$ and integers $p,\;q$.

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"