CraigsMaths

Matrices are simply arrays of values. We use them as a tool to ease operations such as solving simultaneous equations, working with vectors and transformations.

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It is fairly simple to memorise the formula for the determinant of a 2×2 matrix:

Here we look at a simple approach that aids memorising the formula for a 3×3 matrix called Sarrus’ rule which will give you the determinant of a 3×3 matrix.

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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.