Multiplying matrices (pre-defined sizes in answers)

Multiplying matrices (student-defines sizes in answers)

Multiplying matrices (pre-defined sizes in answers)

This set is designed to emphasise non-commutativity.

Multiplying matrices (pre-defined sizes in answers)

Introduces unit/identity matrices

Multiplying matrices (pre-defined sizes in answers)

Zero matrices AND AB = 0 does not imply that either A = 0 or B = 0.

Determinant of 2x2 and notation

Students are asked to form the calculation before giving answer.

Determinant of 2x2 and notation

Input answer only.

Useful properties of determinants that allow simplification.

Choose which of 5 matrices are in a) row echelon form but not reduced b) reduced row echelon form c) neither.

Some basic tests of adding, scaling, and multiplying matrices.

Adding 2x2 matrices. Very simple question. Marks per correct entry.

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.

Demo of automatically generating latex strings to out put vectors/matrices of variable size and that are calculated by some formula.

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.

Adding matrices of random size: two to four rows and two to four columns. Advice (i.e. solution) has conditional visibility to show only the correct size.

Find the size of a matrix.

Matrix addition, with the added test of whether they understand that only matrices of the same size can be added.

Decide if matrix sizes match so they can be added.

Calculate trace of a matrix. Fixed matrices as the same as in our workbook.