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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”.
Example In a 4 x 5 matrix, how many values are present?
What is your answer?
 
Addition:
  • 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.

Example
Find Z
What is your answer?



 
Example
Find Y
What is your answer?



 
Example
Find X
What is your answer?



 
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.

Example
Find W
What is your answer?



 
Example
Find V
What is your answer?



 
Example
Find U
What is your answer?



 
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.

Example
Find T
What is your answer?



 
Example
 Find S
What is your answer?



 



T Rades

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