DP Further Mathematics HL Questionbank
4.6
Description
[N/A]Directly related questions
- 18M.2.hl.TZ0.6c: State which elements of S are self-inverse with respect to \( * \).
- 18M.2.hl.TZ0.6b: Show that every element of S has an inverse with respect to \( * \).
- 18M.2.hl.TZ0.6a: Find the identity element of S with respect to \( * \).
- 16M.2.hl.TZ0.6e: (i) Find the inverse of \(a + b\sqrt 2 \). (ii) Hence show that \({a^2} - 2{b^2}\)...
- 16M.2.hl.TZ0.6d: Show that the subset, \(G\), of elements of \(J\) which have inverses, forms a group of infinite...
- 16M.2.hl.TZ0.6c: Show that (i) \(1 - \sqrt 2 \) has an inverse in \(J\); (ii) \(2 + 4\sqrt 2 \) has no...
- 16M.2.hl.TZ0.6b: State the identity in \(J\).
- 17M.2.hl.TZ0.8c.v: Determine the inverse of the element 3 in \({G_{31}}\).
- 17M.2.hl.TZ0.8c.iv: Determine the inverse of the element 3 in \({G_{11}}\).
- 17M.2.hl.TZ0.8c.iii: Explain why the inverse of the element 3 is \(\frac{1}{3}(n + 1)\) for some values of \(n\) but...
- 17M.2.hl.TZ0.8c.ii: Show that the inverse of the element 2 is \(\frac{1}{2}(n + 1)\).
- 17M.2.hl.TZ0.8a.ii: Show that, for...
- 17M.2.hl.TZ0.8a.i: Show that there are no elements \(a,{\text{ }}b \in {S_n}\) such that \(a{ \times _n}b = 0\).
- 10M.2.hl.TZ0.1a: (i) Show that \( * \) is associative. (ii) Find the identity element. (iii) Find...
Sub sections and their related questions
The identity element \(e\).
- 10M.2.hl.TZ0.1a: (i) Show that \( * \) is associative. (ii) Find the identity element. (iii) Find...
- 16M.2.hl.TZ0.6b: State the identity in \(J\).
- 16M.2.hl.TZ0.6c: Show that (i) \(1 - \sqrt 2 \) has an inverse in \(J\); (ii) \(2 + 4\sqrt 2 \) has no...
- 16M.2.hl.TZ0.6d: Show that the subset, \(G\), of elements of \(J\) which have inverses, forms a group of infinite...
- 16M.2.hl.TZ0.6e: (i) Find the inverse of \(a + b\sqrt 2 \). (ii) Hence show that \({a^2} - 2{b^2}\)...
- 18M.2.hl.TZ0.6a: Find the identity element of S with respect to \( * \).
- 18M.2.hl.TZ0.6b: Show that every element of S has an inverse with respect to \( * \).
- 18M.2.hl.TZ0.6c: State which elements of S are self-inverse with respect to \( * \).
The inverse \({a^{ - 1}}\) of an element \(a\).
- 16M.2.hl.TZ0.6b: State the identity in \(J\).
- 16M.2.hl.TZ0.6c: Show that (i) \(1 - \sqrt 2 \) has an inverse in \(J\); (ii) \(2 + 4\sqrt 2 \) has no...
- 16M.2.hl.TZ0.6d: Show that the subset, \(G\), of elements of \(J\) which have inverses, forms a group of infinite...
- 16M.2.hl.TZ0.6e: (i) Find the inverse of \(a + b\sqrt 2 \). (ii) Hence show that \({a^2} - 2{b^2}\)...
- 18M.2.hl.TZ0.6a: Find the identity element of S with respect to \( * \).
- 18M.2.hl.TZ0.6b: Show that every element of S has an inverse with respect to \( * \).
- 18M.2.hl.TZ0.6c: State which elements of S are self-inverse with respect to \( * \).
Proof that left-cancellation and right cancellation by an element \(a\) hold, provided that \(a\) has an inverse.
- 18M.2.hl.TZ0.6a: Find the identity element of S with respect to \( * \).
- 18M.2.hl.TZ0.6b: Show that every element of S has an inverse with respect to \( * \).
- 18M.2.hl.TZ0.6c: State which elements of S are self-inverse with respect to \( * \).
Proofs of the uniqueness of the identity and inverse elements.
- 16M.2.hl.TZ0.6b: State the identity in \(J\).
- 16M.2.hl.TZ0.6c: Show that (i) \(1 - \sqrt 2 \) has an inverse in \(J\); (ii) \(2 + 4\sqrt 2 \) has no...
- 16M.2.hl.TZ0.6d: Show that the subset, \(G\), of elements of \(J\) which have inverses, forms a group of infinite...
- 16M.2.hl.TZ0.6e: (i) Find the inverse of \(a + b\sqrt 2 \). (ii) Hence show that \({a^2} - 2{b^2}\)...
- 18M.2.hl.TZ0.6a: Find the identity element of S with respect to \( * \).
- 18M.2.hl.TZ0.6b: Show that every element of S has an inverse with respect to \( * \).
- 18M.2.hl.TZ0.6c: State which elements of S are self-inverse with respect to \( * \).
