Description
1. Given a vector of samples � = [−100, −99, … ,99,100], create a vector � calculated based
on element-by-element operations such that �2 = 0.001 �2
‘ + 1. Construct matrix � such
that
� =
�
�
� + �
2. The electric field intensity, �(�), due to a ring of radius � at any point � along the
axis of the ring is given by:
� � = 9604.5
��
�2 + �2
3
2
Given R=6 cm and a row vector � from elements ranging from 2 cm to 6 cm and spacing of
0.01 cm, use element-by-element operations to calculate a row vector � whose elements are
�2 = �(�2). Then construct a matrix of
� = �
�
Hint: use ‘format longg’ to see the significant digits (otherwise you’ll just see 0.0000)
3. The voltage �(�) in Volt and the current �(�) in Amp � seconds after closing the switch in
an RC circuit are given by
� � = 24 1 − �E F
GH
� � = 24
�
�E F
GH
given � = 3800 Ω and � = 4000×10EN F. Create a row vector �, with values of times from 0
to 20 sec with spacing of 2 sec, and use it to create row vectors � and � such that �2 = �(�2)
and �2 = �(�2). Then construct a matrix of
� =
�
�
�
4. Two vectors are given as
� = −1� + 2.5� + 0.5�
� = +1� + 0.2� + 2�
Compute the dot product as � = � ⋅ �.
5. Use cross() to compute the vector cross product as � = ��, where � is a row vector
and � and v are two row vectors defined in question 4.
6. Use Matlab to show that the reciprocals of square numbers produce a convergent series
1
�’
W
XY%
= �’
6
Do this by computing the following sums
� = 1
�’
%[
XY%
, � = 1
�’
\[
XY%
, � = 1
�’
%[[
XY%
and placing your answers in matrix � = � � �
7. Given two matrices
� =
1 −1 1
−1 1 −1
1 −1 1
and � =
10 2 0
3 8 3
1 3 12
Determine � = ���_ where the superscript denotes transpose
8. Given two matrices
� =
1 −3 5
2 2 4
−2 0 6
and � =
0 −2 1
5 1 −6
2 7 −1
Determine � = �E%(� + ��_)
9. Given matrix � =
1 −3 5
2 2 4
−2 5 6
Let � be the matrix formed by having each element of A inverted such that � 2,a = 1/ � 2,a
Then calculate � = ��.
10. The following linear set of equations are determined by applying mesh current analysis
to a circuit. Solve the linear set of equations using the \ operator in Matlab
−44�% + 10�’ + 16�c = −20
10�% − 43�’ + 6�c + 12�d = 0
16�% + 6�’ − 30�c + 8�d = 12
12�’ + 8�c − 34�d = −40
Let � = [�% �’ �c �d] be a row vector of the results.