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Studying for CIE Matrix Further Maths watch

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    Which books would you recommend for studying matrices for CIE further maths? Which other exam board has a similar coverage of matrices as CIE?

    I'm really concerned because the matrix section looks really difficult and I have no idea where to study it from.

    Here is the syllabus for reference:

    • recall and use the axioms of a linear (vector) space
    (restricted to spaces of finite dimension over the field of
    real numbers only);
    • understand the idea of linear independence, and
    determine whether a given set of vectors is dependent
    or independent;
    • understand the idea of the subspace spanned by a given
    set of vectors;
    • recall that a basis for a space is a linearly independent
    set of vectors that spans the space, and determine a
    basis in simple cases;
    • recall that the dimension of a space is the number of
    vectors in a basis;
    • understand the use of matrices to represent linear
    transformations from R R n m " .
    • understand the terms ‘column space’, ‘row space’,
    ‘range space’ and ‘null space’, and determine the
    dimensions of, and bases for, these spaces in simple
    cases;
    • determine the rank of a square matrix, and use (without
    proof) the relation between the rank, the dimension of
    the null space and the order of the matrix;
    • use methods associated with matrices and linear spaces
    in the context of the solution of a set of linear equations;
    • evaluate the determinant of a square matrix and find the
    inverse of a non-singular matrix (2 × 2 and 3 × 3 matrices
    only), and recall that the columns (or rows) of a square
    matrix are independent if and only if the determinant is
    non-zero;
    • understand the terms ‘eigenvalue’ and ‘eigenvector’, as
    applied to square matrices;
    • find eigenvalues and eigenvectors of 2 × 2 and 3 × 3
    matrices (restricted to cases where the eigenvalues are
    real and distinct);
    • express a matrix in the form QDQ−1, where D is a
    diagonal matrix of eigenvalues and Q is a matrix whose
    columns are eigenvectors, and use this expression,
    e.g. in calculating powers of matrices.
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    I am sorry for the late reply. Chapters 1 and 2 in "Linear Algebra and its Applications by Gilbert Stang" cover the first 9 points in the syllabus brilliantly. (All the way from axiom vector spaces till the solving of a set of linear equations). As for the last 4 points, in "Further Pure Mathematics by Brian and Mark Gautler", chapter 5 talks about the evaluation of determinants and chapter 14 gives a good explanation on inverting matrices, eigenvalues and eigenvectors and the diagonalisation of a matrix. Note that you can find everything in the first book I listed, but it may be too rigorous and the second book will do just fine. If you get stuck then you can message me. I wish you the best of luck in your studies!
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    (Original post by InvertA6x6Matrix)
    I am sorry for the late reply. Chapters 1 and 2 in "Linear Algebra and its Applications by Gilbert Stang" cover the first 9 points in the syllabus brilliantly. (All the way from axiom vector spaces till the solving of a set of linear equations). As for the last 4 points, in "Further Pure Mathematics by Brian and Mark Gautler", chapter 5 talks about the evaluation of determinants and chapter 14 gives a good explanation on inverting matrices, eigenvalues and eigenvectors and the diagonalisation of a matrix. Note that you can find everything in the first book I listed, but it may be too rigorous and the second book will do just fine. If you get stuck then you can message me. I wish you the best of luck in your studies!
    Thank you so much for your help
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