DP Further Mathematics HL Questionbank
The definition of a group \(\left\{ {G, * } \right\}\) .
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[N/A]Directly related questions
- 18M.1.hl.TZ0.4b.ii: Show that this group is cyclic.
- 18M.1.hl.TZ0.4b.i: Show that T1, T2, T3, T4 under the operation of composition of transformations form a group....
- 18M.1.hl.TZ0.4a: Copy and complete the following Cayley table for the transformations of T1, T2, T3, T4, under the...
- 11M.2.hl.TZ0.6a: (i) Draw the Cayley table for the set \(S = \left\{ {0,1,2,3,4,\left. 5 \right\}} \right.\)...
- 10M.2.hl.TZ0.1b: The domain of \( * \) is now reduced to \(S = \left\{ {0,2,3,4,5,\left. 6 \right\}} \right.\) and...
- 09M.2.hl.TZ0.2A.a: (i) Show that \({\mathbb{Z}_4}\) (the set of integers modulo 4) together with the operation...
- 09M.2.hl.TZ0.2B.b: the group is cyclic.
- 13M.1.hl.TZ0.2a: Show that \({(ba)^2} = e\) .
- 13M.1.hl.TZ0.2b: Express \({(bab)^{ - 1}}\) in its simplest form.
- 13M.1.hl.TZ0.2c: Given that \(a \ne e\) , (i) show that \(b \ne e\) ; (ii) show that \(G\) is not...
- 13M.2.hl.TZ0.5e: Determine whether the set \(E\) forms a group under (i) the operation of addition; (ii)...
- 07M.1.hl.TZ0.3a: Show that the set \(S\) of numbers of the form \({2^m} \times {3^n}\) , where...
- 07M.2.hl.TZ0.5b: Let \(S\) denote the set...
- 12M.1.hl.TZ0.1a: The set \({{\rm{S}}_1} = \left\{ {2,4,6,8} \right\}\) and \({ \times _{10}}\) denotes...
- SPNone.1.hl.TZ0.14b: Show that \(S\) forms an Abelian group under matrix multiplication.
- SPNone.2.hl.TZ0.4b: Show that \(\left\{ {S,{ \times _9}} \right\}\) is not a group.
- SPNone.2.hl.TZ0.4c: Prove that a group \(\left\{ {G,{ \times _9}} \right\}\) can be formed by removing two elements...
- SPNone.2.hl.TZ0.4e: Solve the equation \(4{ \times _9}x{ \times _9}x = 1\) .
- 14M.2.hl.TZ0.2a: The set \(S\) contains the eighth roots of unity given by...
- 15M.1.hl.TZ0.3b: Show that \(\{ S,{\text{ }}{ + _6}\} \) forms an Abelian group.