348 results for "vector".
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Exam (5 questions) in .Vectors
5 questions on vectors. Scalar product, angle between vectors, cross product, when are vectors perpendicular, combinations of vectors defined or not.
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Question in .Vectors
Curl of a vector field.
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Question in .Vectors
Curl and divergence of a vector field. Determine whether the vector field is irrotational or solenoidal.
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Question in Trigonometry
No description given
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Question in Engineering Statics
Find the sum of two 2-dimensional vectors, graphically and exactly using the parallelogram rule.
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Question in Linear Algebra 1st year
Demo of automatically generating latex strings to out put vectors/matrices of variable size and that are calculated by some formula.
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Question in Linear Algebra 1st year
In this demo question, you can see either 2 or 3 gaps depending on the variable \(m\), and the marking algorithm doesn't penalise for the empty third gap in cases when it is not shown.
Reason to use it: for vectors or matrices containing only numbers, one can easily use matrix entry to account for a random size of an answer. But this does not work for mathematical expressions. There we have to give each entry of the vector as a separate gap, which then becomes a problem when the size varies. This solves that problem. For this reason I've included two parts: one very simple one that just shows the phenomenon of variable number of gaps, and one which is more like why I needed it.
Note that to resolve the fact that when \(m=2\), the point for the third gap cannot be earned, I have made it so that the student only gets 0 or all points, when all shown gaps are correctly filled in.
Note the use of Ax[m-1] in the third gap "correct answer" of part b): if you use Ax[2], then it will throw an error when m=2, as then Ax won't have the correct size. So even though the marking algorithm will ignore it, the question would still not work.
Bonus demo if you look in the variables: A way to automatically generate the correct latex code for \(\var{latexAx}\), since it's a variable size. I would usually need that in the "Advice", i.e. solutions, rather than the question text.
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Question in Linear Algebra 1st year
In this demo question, you can see either 2 or 3 gaps depending on the variable \(m\), and the marking algorithm doesn't penalise for the empty third gap in cases when it is not shown.
Reason to use it: for vectors or matrices containing only numbers, one can easily use matrix entry to account for a random size of an answer. But this does not work for mathematical expressions. There we have to give each entry of the vector as a separate gap, which then becomes a problem when the size varies. This solves that problem. For this reason I've included two parts: one very simple one that just shows the phenomenon of variable number of gaps, and one which is more like why I needed it.
Note that to resolve the fact that when \(m=2\), the point for the third gap cannot be earned, I have made it so that the student only gets 0 or all points, when all shown gaps are correctly filled in.
Note the use of Ax[m-1] in the third gap "correct answer" of part b): if you use Ax[2], then it will throw an error when m=2, as then Ax won't have the correct size. So even though the marking algorithm will ignore it, the question would still not work.
Bonus demo if you look in the variables: A way to automatically generate the correct latex code for \(\var{latexAx}\), since it's a variable size. I would usually need that in the "Advice", i.e. solutions, rather than the question text.
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Question in Linear Algebra 1st year
Abstract linear combinations. "Surreptitious" preview of bases and spanning sets, but not explicitely mentioned. There is no randomisation because it is just an abstract question. For counter-examples, any valid counter-example is accepted.
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Question in Linear Algebra 1st year
Calculate matrix times vector.
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Exam (2 questions) in Linear Algebra 1st year
Easy intro questions to be done when the students have seen the "vector space axioms" but not as axioms, just in the context of \(\mathbb{R}^n\).
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Question in Linear Algebra 1st year
Calculate matrix times vector.
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Question in Linear Algebra 1st year
Calculate matrix times vector.
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Question in Linear Algebra 1st year
First compute matrix times vector for specific vectors. Then determine domain and codomain and general formula for the matrix transformation defined by the matrix.
Randomising the number of rows in the matrix, m, makes the marking algorithm for part c) slightly complicated: it checks whether it should include the third gap or not depending on the variable m. For the correct distribution of marks, it is then necessary to do "you only get the marks if all gaps are correct". Otherwise the student would only get 2/3 marks when m=2, so the third gap doesn't appear.
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Exam (4 questions) in Linear Algebra 1st year
easy vector addition and scalar multiplication, for practice after Section 1 of lectures.
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Question in Linear Algebra 1st year
Abstract linear combinations. "Surreptitious" preview of bases and spanning sets, but not explicitely mentioned. There is no randomisation because it is just an abstract question. For counter-examples, any valid counter-example is accepted.
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Question in Linear Algebra 1st year
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.
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Question in Linear Algebra 1st year
Given vector $\boldsymbol{v}$ find the norm. Since putting in square roots is tricky, actually input the square norm, so it's an integer.
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Question in Linear Algebra 1st year
Given vector $\boldsymbol{v}$ find the norm. Since putting in square roots is tricky, actually input the square norm, so it's an integer.
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Question in Linear Algebra 1st year
Adding vectors of random size. Advice (i.e. solution) has conditional visibility to show only the correct size.
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Question in Linear Algebra 1st year
Calculating with vectors in \(\mathbb{R}^4\), including resolving brackets. The fixed vector size is so that a test is fair to all students.
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Question in Linear Algebra 1st year
Simple scalar multiplication of a general vector with the important scalars 0, 1, -1. Just the variable name is randomised.
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Question in Linear Algebra 1st year
give the negative of each of two vectors. One always has 5 entries, the other has a random number of entries.
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Question in Linear Algebra 1st year
Simple vector addition and scalar multiplication in \(\mathbb{R}^2\).
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Question in Linear Algebra 1st year
Adding and subtracting vectors of random size, including resolving brackets. Advice (i.e. solution) has conditional visibility to show only the correct size.
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Question in Linear Algebra 1st year
Calculate matrix times vector.
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Question in Linear Algebra 1st year
First compute matrix times vector for specific vectors. Then determine domain and codomain and general formula for the matrix transformation defined by the matrix.
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Question in Linear Algebra 1st year
First compute matrix times vector for specific vectors. Then determine domain and codomain and general formula for the matrix transformation defined by the matrix.
Randomising the number of rows in the matrix, m, makes the marking algorithm for part c) slightly complicated: it checks whether it should include the third gap or not depending on the variable m. For the correct distribution of marks, it is then necessary to do "you only get the marks if all gaps are correct". Otherwise the student would only get 2/3 marks when m=2, so the third gap doesn't appear.
-
Question in Linear Algebra 1st year
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 Linear Algebra 1st year
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.