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Problem Metadata

Date: November 11, 2025

Problem Number: #1

Problem Curator: @Phanie

lymphoidcell - Overview

Indonesian version: Daily Math - HARI 1

Vector Equality in ℝⁿ

Category: Machine Learning Math - Linear Algebra

Difficulty Level: Beginner

Problem Statement

(a) The following are vectors:

$(2, -5), (7, 9), (0, 0, 0), (3, 4, 5)$

The first two vectors belong to $ℝ²$, whereas the last two belong to $ℝ³$.

The third is the zero vector in $ℝ³$.

(b) Find $x, y, z$ such that $(x - y, x + y, z - 1) = (4, 2, 3)$.

By definition of equality of vectors, corresponding entries must be equal.

$$ x - y = 4, x + y = 2, z - 1 = 3 $$