CraigsMaths

This is the “standard” form of the quadratic equation:

where

This article will describe how to find the vertex, x-intercepts and y-intercepts for this form of a quadratic equation.

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Given a system of simultaneous equations in matrix form

Where is an invertable n x n square matrix, is a variables column matrix containing and is a constants matrix containing .

Then can be found with Cramer’s rule,

Where is formed by replacing the ith column of with .

Determinants are only defined for square matrices. This article states the formulae for a 2×2 matrix, a 3×3 matrix and the general case. The general case is used when finding determinants of 4×4 matrices or bigger and most often when solving simultaneous equations. These large matrices involve quite a deal of computation and in real world situations would usually be solved by computers.

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Square matrix - The number of rows and number of columns are equal.

Diagonal matrix - All elements other than those in the main diagonal are 0.

Identity matrix - The identity matrix is a diagonal matrix where all elements of the main diagonal are 1.

Scalar matrix - A diagonal matrix with all diagonal elements alike.

Row matrix - The matrix consists of a single row of elements.

Column matrix - The matrix consiste of a single column of elements.

Symmetric matrix - A square matrix which is equal to its transpose.

Skew-symmetric matrix - A square matrix which is equal to the opposite of its transpose.