BitWithBite
Mathematics Worksheet
🌐 Vector Spaces
SCORE___ / 20
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After this worksheet you can
Test vectors for linear independence.Find the dimension of a space.Recognise a basis.Understand the span of a set of vectors.📚 Quick Recap
A vector space is a collection of objects (vectors) that can be added together and scaled, following a consistent set of rules — an abstraction that unifies everything from arrows in space to functions and polynomials.
🧠 Section A · Concept Check ● BEGINNER 4 × 1 = 4
1Is {(1,3),(2,6)} linearly independent?
2Is {(1,0),(1,1)} linearly independent?
3The dimension of a space with basis {(1,0,0),(0,1,0)} is:
4Does the span of {(1,0),(0,1)} cover all of 2D space?
🧮 Section B · Problem Solving ● INTERMEDIATE 2 + 3×3 = 11
5Vectors that are not scalar multiples of each other are linearly .
6{(1,3),(2,6)} is linearly (since (2,6) = 2(1,3)).
7Is {(1,3),(2,6)} linearly independent?
8Is {(1,0),(1,1)} linearly independent?
9What is the dimension of a vector space with basis {(1,0,0),(0,1,0)}?
🚀 Section C · Challenge ● CHALLENGE 5
10Does the span of {(1,0),(0,1)} cover all of 2D space?
💭 Reflection — the most useful thing I learned:
A ___/4 B ___/11 C ___/5 Total ___/20
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✂ answer key — fold or cut before handing out
1-A 2-A 3-A 4-A | 5 independent 6 dependent 7 = No, since (2,6) = 2(1,3) 8 = Yes, neither is a scalar multiple of the other 9 = 2 | 10 = Yes