Write the keyword
Given

Specify the initial values of the variables

Solve the same system by the Find block

Method 3: Using the
Given .. Find block

or, the vector x

Thus, we can display the components of x

An alternative way to read the solution is to assign
the elements of the last column of the reduced matrix
rrefA to the components of a vector x:

Display the computed solution

Define the solution

Display the coefficient matrix A

and the vector b as defined above

The system A x = b can be solve by left-multiplying
both sides of the equation by the inverse of A. Then
the solution x is obtained from the equation x = A-1 b

we can use the inverse matrix method.

Now that we know that

Compute the determinant of A

Knowing that the coefficient matrix A is a square matrix,
we can solve the system by the inverse matrix method
if A is invertible. We can find if A is invertible
by computing the determinant of the A (can you think
of another way to find if A is invertible?).

Method 4: Using the inverse of the matrix

Remark

The computed values are not assigned to the variables
x, y and z. To assigned the values to a variable, say,
s1, we replace the Find(x, y, z) above with s1 := Find(x,
y, z), then display s1.

Define the equations

Remark:

you have to use the boolean equal

(Ctrl + =) to define the equations.

Or refer to its components using double subscripts (since
it is a row vector)

This way we can display the solution

The solution obtain above is not stored in a variable.
To assign the results to a variable s we do the following

Notice that the results are returned using exact arithmetic.
To see the results in floating (decimal) format we
type = after the results as follows:

3. In the placeholder provided by the solve command
type the names of the variables (separated by commas)
to solve for

==>

==>

To solve a system of n equations using the solve command
we do

1. Create an n x 1 vector and write the equations as
the components of this vector

2. Click on any of the equations and use the math toolbar
as follows:

Method 1: Using the solve
command

Since Mathcad starts the subscripts from 0 and we are
used to starting it from 1, we assign 1 to the keyword
ORIGIN

Methods of solving linear systems using Mathcad

If the system has a unique solution, there will be a
leading entry in the reduced matrix for each variable.
In this case we have a leading entry for each of the
three variables. So, we read the solution from the
last column of rrefA as:

Display the reduced matrix

Compute the row reduced echelon form of

the augmented matrix

Display the augmented matrix

Augment A and b and name it Ab

Define the right-hand side as vector b

Define the coefficient matrix as A

Method 2: Using the rref
command

Then we can refer to the solution by the components
of x using only one subscript

To obtain the solution in a column vector form, we assign
the transpose of s to a variable, say, x