 Site Navigation                          Basic Operations with Matrices
Properties of Matrices
• A matrix is a rectangular array of values consisting of intersecting rows and columns.
• An upper-case variable is used to represent a unique matrix much like a lower-case variable represents a unique value.
• The dimensions of a matrix are stated as the number of rows by the number of columns.

Example • The name of the matrix in this example is Matrix X.
• The variable assigned to this matrix is arbitrary and is independent from that of the contained values.
• Matrix X is a 2 x 3 matrix.
• When verbalizing the dimensions of a matrix, read them like you would the dimensions of lumber or a room. This example would be read as “two by three”. In a 4 x 5 matrix, how many values are present? What is your answer? • Only matrices with equal dimensions can be added.
• The addition of matrices is commutative. A + B = B + A
• The addition of matrices is associative. (A + B) + C = A + (B + C)

Examples
We will use the following three matrices do complete the example problems.     Find Z What is your answer?       Find Y What is your answer?       Find X What is your answer? No Solution Exists    Subtraction:
• Only matrices with equal dimensions can be subtracted.
• Subtraction of matrices is not commutative. • If one looks at subtraction as the addition of a negative, then the equation is commutative. • Subtraction of matrices is not associative. • If one looks at subtraction as the addition of a negative, then the equation is associative. Examples
We will use the following three matrices do complete the example problems.     Find W What is your answer? No Solution Exists     Find V What is your answer?   No Solution Exists   Find U What is your answer?  No Solution Exists  Scalar Multiplication:
• A number that is multiplying the matrix is called a Scalar
• The multiplication of a matrix and a scalar is commutative. • The multiplication of a matrix and a scalar is associative. • If dividing by a value, multiply by the value's inverse. Examples
We will use the following three matrices do complete the example problems.     Find T What is your answer?       Find S What is your answer?   No Solution Exists Show Related AlgebraLab Documents AlgebraLAB
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