Sums of Integers, Squares & Cubes How can we use sigma notation? When writing the sum of a series you can use sigma notation The series can instead be written as This means “the sum of all the...
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...
