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
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and then transpose again
. For example, the second row of matrix A is obtained
as follows:
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
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
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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
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
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since x is not
subscripted.
Create a range variable y from 2 to 3 with increment
0.2
In general, a set of values in the closed interval [a,
b] with increment incr can be created by
Create a range variable z from 10 to 6 with decrement
0.5
(Or
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)
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
Notice that the elements that were not assigned values
are set to 0 by Mathcad
A 3 x 2 matrix with all elements equal to 0 is created
by
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:
Or type x : 1 then use the Arithmetic Palette and
choose Range Variable
Note that the fist element of the vector is named
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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
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is not defined and
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will be the name of the first component of the vector
From now on all subscripts of vectors and matrices will
start from one.
Create two vectors a and b
Multiply the vector a scalar 2
Compute the length of a vector
Introduction to Mathcad Vectors and Matrices
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)
Fill in the place holders "
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" 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
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
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
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 |
Another way to compute the length of a vector (using
the definition)
Create a 3 x 2 matrix A and a 2 x 3 matrix B
Multiply Matrix A by a scalar
Every element is multiplied by 3
Compute the transpose
of the matrix B