CraigsMaths

Multiplying matrices is fairly simple but there is a process to learn and a couple of rules to remember.

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Matrix addition and subtraction is fairly simple. Just remember that we can only add or subtract matrices if they have the same dimensions. The number of rows must be equal in each matrix and the number of columns must be equal in each matrix.

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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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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 .

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.