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# Studying for CIE Matrix Further Maths watch

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1. 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.
2. 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!
3. (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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