VECTORS AND MATRICES

 

1. Vectors can be written both in row form like this:   2. or in column format like this:

A (m x n) matrix:

 

A matrix is a rectangular arrangement of mathematical expressions that can be simply numbers. The horizontal and vertical lines in a matrix are called rows and columns, respectively. The numbers in the matrix are called its entries or its elements. To specify the size of a matrix, a matrix with m rows and n columns is called an m -by- n matrix or m × n matrix, while m and n are called its dimensions.

A matrix with one row (a 1 × n matrix) is called a row vector, and a matrix with one column (an m × 1 matrix) is called a column vector.

 

Vectors and Matrices
In writing	Pronunciation	Rule
A 1 x 3 vector	1-by-3 vector	the first entry (1) is the number of rows while the second entry (3) is the number of columns
A 2 x 3 matrix	2-by-3 matrix	2 is the number of rows, 3 is the number of columns
A m x n matrix	m -by- n matrix	m is the number of rows, n is the number of columns
A n x n matrix (a square matrix)	n -by- n matrix	when the numbers of rows and columns are equal

Matrices are usually denoted using upper-case letters, while the corresponding lower-case letters, with two subscript indices, represent the entries. The entry in the i-th row and the j-th column of a matrix is typically referred to as the i,j, (i,j), or (i,j) th entry of the matrix. For example, the (i, j) th entry of a matrix A is most commonly written as a . Alternative notations for that entry are A [ i,j ] or A .

http://www.answers.com/topic/matrix-mathematics

Vectors and matrices are really important in applied mathematics. Engineers and scientists use them to solve challenging problems in many dimensions. MathCAD’s matrix and graphing tools offer capabilities that can help to explore vectors and matrices. With currently available technologies matrices can be used, explored, and visualized effectively.

To create a vector or matrix in MathCAD:

1) Type [Ctrl] M or click the Matrix or Vector button on the Matrix toolbar.

2) Enter the dimensions of the vector or matrix you want and click OK or Insert.

3) Fill in each empty placeholder with a value. Use the Tab key to move from placeholder to placeholder.

1) Answer the following questions:

1) How many components do these vectors have and are they row or column vectors?

 

a) c)

b) d)

 

2) How do you write the dimensions of these matrices:

 

a) ; write down and name the (2,3) entry of this matrix.

 

b) ; write down and name the (3,4) entry and the (1,3) entry of this matrix

 

c) ; write down and name the (2,1) entry of this matrix

 

Use MathCAD to solve the following problems, pronounce them:

3) If, calculate:

a) 3· v

b) 1.2· v

c)

 

4) If, calculate:

a) -3·A

b) 17·A

c)

5) If, and calculate v + w; v w.

6) If, and calculate v + w; v w.

 

7) If, and calculate v + w; v w.