Linear Transformations of Roots What is a Linear Transformation? A linear transformation can be expressed as ?where: w?is the new root x?is the original root p?and?q?are constants If you perform a ...
Roots of Quadratics How are the roots of a quadratic linked to its coefficients? Because a quadratic equation ? (where ) has roots and , you can write this equation instead in the form Note that It...
Invariant Points What is an invariant point? When applying transformations to a shape or collection of points, there may be some points that stay in their original position; these are known as?inva...
2D Transformations What is meant by a 2D geometric transformation? The following transformations can be represented (in 2D) using?multiplication?of a?2x2?matrix rotations (about the origin) reflect...
Transformations using a Matrix What is a transformation matrix? A transformation matrix is used to determine the coordinates of an?image?from the?transformation?of an?object reflections, rotations,...
Inverse of a Matrix What is an inverse of a matrix? The determinant can be used to find out if a matrix is invertible or not: If , then ?is?invertible If , then ?is singular and does?not?have an in...
Determinant of a 2x2 Matrix What is a determinant? The?determinant?is a?numerical value?(positive or negative) calculated from the elements in a matrix and is used to find the?inverse?of a matrix Y...
Introduction to Matrices Matrices are a useful way to represent and manipulate data in order to model situations. The elements in a matrix can represent data, equations or systems and have many rea...
Roots of Complex Numbers How do I find the square root of a complex number? The square roots of a complex number will themselves be complex: i.e. if We can then square and equate it to the original...
