Matrices

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Find invariant points and lines for a linear transformation. Calculate determinants of 2 x 2 and 3 x 3 matrices and interpret as scale factors, including the effect on orientation. Understand and use singular and non-singular matrices. Properties of inverse matrices. Calculate and use the inverse of non-singular 2 x 2 matrices and 3 x 3 matrices. Solve three linear simultaneous equations in three variables by use of the inverse matrix. Interpret geometrically the solution and failure of solution of three simultaneous linear equations.