BitWithBite
Mathematics Worksheet
🔄 Linear Transformations
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After this worksheet you can
Apply a matrix to a vector.Recognise scaling, reflection, rotation and shear.Use the identity transformation.Understand composition order.📚 Quick Recap
A linear transformation is a function between vector spaces that preserves addition and scalar multiplication — and every one of them can be represented by a matrix.
🧠 Section A · Concept Check ● BEGINNER 4 × 1 = 4
1A = [[4,0],[0,4]], v = (1,3). T(v) =?
2A = [[−1,0],[0,1]], v = (5,2) (reflect over y-axis). T(v) =?
3A = [[0,−1],[1,0]], v = (3,4) (90° rotation). T(v) =?
4A = [[1,2],[0,1]], v = (1,1) (shear). T(v) =?
🧮 Section B · Problem Solving ● INTERMEDIATE 2 + 3×3 = 11
5A linear transformation is applied by multiplying the matrix by the .
6A = [[4,0],[0,4]] scales every vector by .
7A = [[4,0],[0,4]]. Find T(v) for v = (1,3).
8A = [[−1,0],[0,1]]. Find T(v) for v = (5,2). (reflect over y-axis)
9A = [[0,−1],[1,0]]. Find T(v) for v = (3,4). (90° rotation)
🚀 Section C · Challenge ● CHALLENGE 5
10A = [[1,2],[0,1]]. Find T(v) for v = (1,1). (shear)
💭 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 vector 6 4 7 = (4,12) 8 = (−5,2) 9 = (−4,3) | 10 = (3,1)