Matrices (paper 1)

Worked examples (6)

• 1Stating orders and testing conformability
• 2Evaluating 2A − 3B element by element
• 3A 2×2 matrix product
• 4A non-square product (2×3)(3×2)
• 5Showing AB ≠ BA
• 6Verifying associativity (AB)C = A(BC)

Model answers (6)

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Worked examples (6)

• 1Recognising the identity matrix
• 2Adding the zero matrix
• 3Verifying that AI = A
• 4Computing A² for a square matrix
• 5Computing A³ in two stages
• 6A non-zero product giving the zero matrix

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Worked examples (6)

• 1Image of a point under a given matrix
• 2Writing down a rotation matrix
• 3Composition of two transformations (order matters)
• 4Finding the matrix from a geometric description
• 5Area scale factor from the determinant
• 6Rotation by a general angle and its inverse

Model answers (6)

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Worked examples (6)

• 1Confirming the origin is invariant
• 2Line of invariant points vs invariant line for a reflection
• 3When the origin is the only invariant point
• 4Finding a line of invariant points
• 5Finding invariant lines y = mx + c (full method)
• 6Invariant lines through the origin (c = 0)

Model answers (6)

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Worked examples (6)

• 1Inverse of a 2×2 matrix — and verifying it
• 2Inverse of a 2×2 matrix with a fractional result
• 3Recognising a singular matrix
• 4Solving simultaneous equations with x = A⁻¹b
• 5Inverse of a 3×3 matrix via cofactors and the adjugate
• 6The reverse-order law (AB)⁻¹ = B⁻¹A⁻¹

Model answers (6)

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Worked examples (6)

• 1Determinant of a 2×2 matrix
• 2Determinant of a 3×3 by cofactor expansion
• 3Deciding singular vs non-singular
• 4Determinant as an area scale factor
• 5Find k so that the matrix is singular
• 6Using det(AB) = det(A) det(B)

Model answers (6)

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