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Problem Metadata

Date: November 12, 2025

Problem Number: #2

Problem Curator: @Phanie

lymphoidcell - Overview

Indonesian version: Daily Math - HARI 2

Basic Vector Operations in ℝ³

Category: Machine Learning Math - Linear Algebra

Difficulty Level: Beginner

Problem Statement

(a) Vector addition and scalar multiplication

Let $u = (2, 4, -5)$ and $v = (1, -6, 9)$.

Then find:

$$ u + v $$

$$ 7u $$

$$ -v $$

$$ 3u - 5v $$

(b) The zero vector identity

The zero vector $0 = (0, 0,...,0)$ in $Rⁿ$ is similar to the scalar $0$ in that, for any vector $u = (a₁, a₂,...,aₙ)$, show that:

$$ u + 0 = u $$