Write the system equations here. The first equation
is written for you
<== this is to reset the values of c1,c2 and c3.
Do not remove these assignments.
Method 2
: Answer the question by using the "given ......find"
command to solve the system
c1 u + c2 v + c3 w = t
For comparison, t is displayed here for you
Step 5: Verify your answer: The is, compute c1 u +
c2 v + c3 w and compare it with t
Are the constants zeros? Why? ==> No. Because the
vectors are linearly dependent
b) Find the constants c1, c2 and c3 such that c1 v1
+ c2 v2 + c3 v3 = 0
Step 6: Compute the row reduced echelon form of A to
verify that the rank is as computed by Mathcad
Step 5: Explain why the vectors are linearly dependent
or linearly independent
==> The rank is less than the number of vectors ==>
they are linearly dependent.
Step 4: Click next to the arrow head and give the definition
of the rank of a matrix
==> The rank is equal to the number of nonzero rows
in the reduced row echelon form of the matrix
Step 3: Use Mathcad rank() command to compute the rank
of the matrix A
Step 2: Display the matrix A here ==>
Step 1: Use the augment command to form the matrix
A = [ v1 v2 v3]
a) Decide if the vectors are linearly dependent or linearly
independent by computing the rank of the matrix
A =[v1 v2 v3], then verify the answer by computing
the row reduced echelon form of A
Step 2: Display the matrix M
Step 1 :Use the augment command to form a matrix M =
[t u v w] of the vectors t, u, v and w.
For example to augment the vectors t, u, and
v we use
a) We know that a set of n+1 vectors in an n-dimensional
vector space are linearly dependent Use the
row reduced echelon form command (rref () ) in Mathcad
to verify that the the vector t, u, v, and w are
linearly dependent
Instructions:
1.
Before you start working on the worksheet, make a copy
of it. This can be done by saving the worksheet
with a new name.
2
.
To facilitate the grading of the project, type your
answers after the arrow (==>) placed in every
question.
3
. Do not delete any pre-assigned variables.
4.
Do not add or delete lines into the document. Enough
room is given for writing your answers.
5.
If for some reason the screen display gets missed up,
press Ctrl+R to refresh the screen display.
6
. Frequently save your worksheet to avoid the loss of
your work
Computer Project One Solution
Step 4: Give the values of the constants
Step 3: Compute the row reduced echelon form
Step 2: Display the matrix A
Step 1: Form the augmented matrix A
Method 1: Augment the vectors in a matrix A, then use
the row reduce echelon form of the augmented matrix
to find the constants c1, c2, c3 such that t = c1 u
+ c2 v +c3 w
b) Express the vector t as a linear combination of the
vectors u, v and w
Explain how the row reduced echelon form is use to verify
the linear dependence of the vectors
Click next to the arrow to write your answer
==> A set of vectors are linearly dependent if one
of them can be written as a linear combination of the
others. That is, if we can find a solution to the nonhomogeneous
system
c1 t +
c2 u + c3 v = w
Step 3: Use the rref( ) command to compute the row reduced
echelon form
