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Truth tables 4 (v2)
Create a truth table for a logical expression of the form $((a \operatorname{op1} b) \operatorname{op2}(c \operatorname{op3} d))\operatorname{op4}e $ where each of $a, \;b,\;c,\;d,\;e$ can be one the Boolean variables $p,\;q,\;r,\;\neg p,\;\neg q,\;\neg r$ and each of $\operatorname{op1},\;\operatorname{op2},\;\operatorname{op3},\;\operatorname{op4}$ one of $\lor,\;\land,\;\to$.
For example: $((q \lor \neg r) \to (p \land \neg q)) \land \neg r$
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Simplex method  4 or 5 random inequalities
Abstract simplex method question. Given optimal tableau, student must identify optimal solution and objective value.
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Simplex algorithm  bus company
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.
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Finding bases for the null space and row space of a matrix
Given a matrix in row reduced form use this to find bases for the null, column and row spaces of the matrix.
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Find n such that $\sigma(n)$ is the given number
Given $m \in \mathbb{N}$, find values of $n\in \mathbb{N}$ such that $\sigma(n)=m$.
There are at most two such solutions in this question.
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Last modified 16/05/2019 14:25
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Find determinant of a 3x3 matrix with a free variable by row reduction
Given a 3x3 matrix with very big elements, perform row operations to find a matrix with singledigit elements. Then reduce that to an upper triangular matrix, and hence find the determinant.
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