40 results.
-
Question in Ugur's workspace
A,B 2×2 matrices. Find eigenvalues and eigenvectors of both. Hence or otherwise, find Bn for largish n.
-
Ugur's copy of Find eigenvalues, characteristic polynomial and a normalised eigenvector of a 3x3 matrix Ready to useQuestion in Ugur's workspace
Given a 3 x 3 matrix, and two eigenvectors find their corresponding eigenvalues. Also fnd the characteristic polynomial and using this find the third eigenvalue and a normalised eigenvector (x=1).
-
Characteristic poly, eigenvalues and eigenvectors 3x3, digonailsability (non-randomised) Ready to useQuestion in Ugur's workspace
Example of an explore mode question. Student is given a 3x3 matrix and is asked to find the characteristic polynomial and eigenvalues, and then eigenvectors for each eigenvalue. The part asking for eigenvectors can be repeated as often as the student wants, to be used for different eigenvalues.
Assessed: calculating characteristic polynomial and eigenvectors.
Feature: any correct eigenvalue will be recognised by the marking algorithm, even multiples of the obvious one(s) (which can be read off from the reduced row echelon form)
Randomisation: Not randomised, just using particular matrices. I am still working on how to randomise this for 3x3; a randomised 2x2 version exists. I have several different versions for 3x3 (not all published yet), so I could make a random choice between these in a test.
The implementation uses linear algebra functions such as "find reduced echelon form" or "find kernel of a reduced echelon form", from the extension "linalg2".
-
Question in Content created by Newcastle University by
Newcastle University Mathematics and Statistics
Real numbers a,b,c and d are such that a+b+c+d=1 and for the given vectors v1,v2,v3,v4 av1+bv2+cv3+dv4=0. Find a,b,c,d.
-
Find forces required to hold a particle in equilibrium when subjected to a downward load. Directions of the reactions are given.
-
Ugur's copy of Find points of intersection, tangents, and angles between parametric curves Ready to useQuestion in Ugur's workspace
Intersection points, tangent vectors, angles between pairs of curves, given in parametric form.
-
Example of an explore mode question. Student is given a 3x3 matrix and is asked to find the characteristic polynomial and eigenvalues, and then eigenvectors for each eigenvalue. The part asking for eigenvectors can be repeated as often as the student wants, to be used for different eigenvalues.
Assessed: calculating characteristic polynomial and eigenvectors.
Feature: any correct eigenvalue will be recognised by the marking algorithm, even multiples of the obvious one(s) (which can be read off from the reduced row echelon form)
Randomisation: Not randomised, just using particular matrices. I am still working on how to randomise this for 3x3; a randomised 2x2 version exists. I have several different versions for 3x3 (not all published yet), so I could make a random choice between these in a test.
The implementation uses linear algebra functions such as "find reduced echelon form" or "find kernel of a reduced echelon form", from the extension "linalg2".
-
No description given
-
Checking whether a given set is a plane or not. Depends on whether two vectors are parallel or not. Then checking whether the plane goes through the origin. This is not always obvious from the presentation.
Not randomised because it's the same as in our workbook.
-
To understand matrix multiplication in terms of linear combinations of column vectors.
-
Checking whether a given set is a plane or not. Depends on whether two vectors are parallel or not. Then checking whether the plane goes through the origin. This is not always obvious from the presentation.
Not randomised because it's the same as in our workbook.
-
Question in Hayley's workspace
Find eigenvalues and eigenvectors of A 2×2 matrix.
-
Question in Bill's workspace
When are vectors \boldsymbol{A,\;B} perpendicular?
-
Question in Bill's workspace
Determine if various combinations of vectors are defined or not.
-
Question in Bill's workspace
Given vectors \boldsymbol{A,\;B}, find \boldsymbol{A\times B}
-
Question in Bill's workspace
Given vectors \boldsymbol{A,\;B}, find the angle between them.
-
Question in Bill's workspace
Given vectors \boldsymbol{A} and \boldsymbol{B}, find their inner product.
-
Question in Content created by Newcastle University by
Newcastle University Mathematics and Statistics
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 by
Newcastle University Mathematics and Statistics
and 1 other
Find minimum distance between a point and a line in 3-space. 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 by
Newcastle University Mathematics and Statistics
and 1 other
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.
-
Question in Content created by Newcastle University by
Newcastle University Mathematics and Statistics
Given vectors \boldsymbol{v,\;w}, find the angle between them.
-
Question in Content created by Newcastle University by
Newcastle University Mathematics and Statistics
and 1 other
Given two 3 dim vectors, find vector equation of line through one vector in the direction of another. Find two such lines and their point of intersection.
-
Question in Content created by Newcastle University by
Newcastle University Mathematics and Statistics
Given vectors \boldsymbol{A,\;B}, find \boldsymbol{A\times B}
-
Question in Content created by Newcastle University by
Newcastle University Mathematics and Statistics
and 1 other
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 by
Newcastle University Mathematics and Statistics
Determine if various combinations of vectors are defined or not.
-
Question in Content created by Newcastle University by
Newcastle University Mathematics and Statistics
and 1 other
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 by
Newcastle University Mathematics and Statistics
and 1 other
A plane goes through three given non-collinear points in 3-space. 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 by
Newcastle University Mathematics and Statistics
and 1 other
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 by
Newcastle University Mathematics and Statistics
Given vectors \boldsymbol{v} and \boldsymbol{w}, find their inner product.
-
Question in Content created by Newcastle University by
Newcastle University Mathematics and Statistics
and 1 other
Intersection points, tangent vectors, angles between pairs of curves, given in parametric form.
