d) Show that the vector w is a solution to the system.
Create the vector w (righ-to-left digits of sn x basis
vectors)
Augment the vector w to the basis vectors
Hint : Use a nested augment command to augment more
than one vector. For example, to augment v1, v2, and
w, use: augment(augment(v1,v2),w). Place the augmented
vectors in a matrix (call it M), and then try to answer
the question.
Compute the rref of M ==>
Give the reason for the vector w being a solution:-
e) Using the previous step, find the constants c1, c2,
... such that the vector w in part (d) is a linear
combination of the basis vectors.
Note: The number of constants will depend on the number
of basis vectors.
f) Use the computed constants in part (e) to verify
that the vector w is a linear combination of the basis
vectors.
Instructions:
0.
Your student number will be used to generate the question
for you. So, type your student number in
the placeholder defining the variable Student_ID.
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 jargoned,
press Ctrl+R to refresh the screen.
Given the homogenous linear system
where A is the 7x7 matrix
a) Compute the rank of the matrix
b) Compute the row reduced echelon form of the matrix
A
c) Give a basis for the solution space by filling the
placeholder in the vectors below.
Note: If you only have two basis vectors, fill-in
the placeholders in v1
and v2
, and leave the rest of the vectors untouched.
