In the above example we extracted a submatrix from row 1 to row 2 and from column 2 to column 3

Thus, to extract a row of a matrix we use the submatrix command. For example to extract the second row of matrix A above we use

Note: The command cols( ) is used so that we get all the columns of the matrix.

Another way to get a row of a matrix is to first transpose the matrix then use the Matrix Column command and then transpose again . For example, the second row of matrix A is obtained as follows:

Details:

Use the augment( ) command to join tow matrices horizontally (side by side)

Use the stack( ) command to join two matrices vertically (one on top of the other)

Use the rref( ) to computer the reduced row echelon form of a matrix

Use the rank( ) command to compute the rank ( = the number of nonzero rows) of a matrix

Use the identity( ) command to create a 3 x 3

identity matrix

Create a 4 x 3 matrix

Use the rows( ) command to find the

number of rows in matrix A

Use the cols( ) command to find the

number of columns in matrix A

Use the Matrix Column command to

extract column j of the matrix

key: A ctrl 6 then type the column number in the

place holder

Or type A then use the Vector and Matrix Palette and click on

==>

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Note: Mathcad does not have a command to extract a row from a matrix, but it can be done in an indirect way as will be shown later.

Use the command submatrix( ) to extract a

submatrix of a matrix

The command format is a follows:

submatix(matrix name, from_row, to_row, from_column, to_column)

Note: Unlike vectors, no subscripts are assigned to the variable x

Mathcad will not display since x is not

subscripted.

Another example:

Create a range variable y from 2 to 3 with increment 0.2

key: y : 2, 2+.2 ; 1

Display y

In general, a set of values in the closed interval [a, b] with increment incr can be created by

Examples

Create a range variable z from 10 to 6 with decrement 0.5

(Or )

Create a diagonal matrix D whose diagonal elements are all -3

Other ways to define a matrix

A matrix can be defined by assigning values to its elements

(key: C [ 1, 1 : 3)

Notice that the elements that were not assigned values are set to 0 by Mathcad

Display the matrix

A 3 x 2 matrix with all elements equal to 0 is created by

Range Variable

A variable with incremental values can be created by what Mathcad calls "range variable". For example, a variable x with values 1, 2,3 ...10 is created as follows:

key: x : 1 ; 10

Or type x : 1 then use the Arithmetic Palette and choose Range Variable

Display x (type x =)

Note that the fist element of the vector is named not

To force Mathcad to start the subscription from 1 rather than zero, we type the keyword: ORIGIN and assign the value 1 to it (we only have to do this once at the beginning of the worksheet.)

Now is not defined and will be the name of the first component of the vector

From now on all subscripts of vectors and matrices will start from one.

Vector Operations

Create two vectors a and b

Add the two vectors

key: a+b=

Multiply the vector a scalar 2

key: 2*b=

Compute the length of a vector

Introduction to Mathcad Vectors and Matrices

The keyword ORIGIN

Mathcad uses 0 as the first subscript of vectors and matrices. For example, to create a 3 x 1 vector type the name of the vector then press the colon ":" key then press Control M. choose the number of rows (3) and columns (1). You get

keyboard keys: a : ctrl m (or use the Vector and Matrix Palette then click on the icon Matrix or Vector)

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Fill in the place holders " " with the values of the vector's elements

Display the elements of the vector

keyboard keys: a [ 0 =

Or type a then use the Arithmetic Palette and click on

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keyboard keys: a [ 1 =

key: B ctrl 1

or use the Vector and Matrix Palette and choose Matrix Transpose

Note: This is not B to the power T

Compute the product BA and define it as P

key: P : B*A

Display the product

key: P=

Compute the determinant of P

key: | then type the name of the vector

and press =

Or type P then use the Vector and Matrix Palette and click on | x |

Compute the inverse of the P

key: P ^ -1

(^ is shift 6)

Special matrix commands

Create a 3 x 1 vector v

Use the diag( ) command to create a diagonal

matrix with vector v as its diagonal.

key: | then type the name of the vector

and press =

Or type P then use the Vector and Matrix Palette and click on | x |

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Another way to compute the length of a vector (using the definition)

Matrix Operations

Create a 3 x 2 matrix A and a 2 x 3 matrix B

Multiply the matrices

key: A*B=

Multiply Matrix A by a scalar

Every element is multiplied by 3

Compute the transpose of the matrix B