Maths Olympiad Prep

Library / CEMC Cayley /191 of 470

CEMC Cayley

Algebra Difficulty 1.8 Junior Find the answer

Calculate the value of (3,1)∇(4,2)(3,1) \nabla (4,2) using the operation ' ∇\nabla ' defined by (a,b)∇(c,d)=ac+bd(a, b) \nabla (c, d)=ac+bd.

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

From the definition, (3,1)∇(4,2)=(3)(4)+(1)(2)=12+2=14(3,1) \nabla (4,2)=(3)(4)+(1)(2)=12+2=14.

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: Omni-MATH, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.