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LearnEdexcel9FM0First teaching 2017Paper 1 · Core Pure Mathematics 1Matrices
Paper 1 · Module

Matrices

2 subtopics≈ 90 min in total
Start the module: Matrix algebra and inversesOpen graphing calculator

  1. Matrix algebra and inverses

    Matrices multiply row-by-column. The determinant measures how a matrix scales area (or volume); when it is zero the matrix has no inverse. For 2×22\times2, A−1=1ad−bc(d−b−ca)\mathbf A^{-1}=\frac1{ad-bc}\begin{pmatrix}d&-b\\-c&a\end{pmatrix}, and inverses solve systems of equations in one step.

    ≈ 45 min

  2. Transformations, invariant points and lines

    The columns of a transformation matrix are the images of the unit vectors i\mathbf i and j\mathbf j. Rotations, reflections, enlargements and stretches all have standard matrices. BA\mathbf{BA} means "do A\mathbf A, then B\mathbf B". Invariant points satisfy Mx=x\mathbf M\mathbf x=\mathbf x; invariant lines map onto themselves.

    ≈ 45 min