A%20mass%20(weight%2020N)%20is%20suspended%20by%20two%20wires%20as%20shown%20in%20the%20figure:%20relevant%20distances%20are%20also%20marked.%20T1%20and%20T2%20are%20the%20tensions%20in%20the%20wires.

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Matrix Algebra - Tutorial 1
1.
A mass (weight 20N) is suspended by two wires as
shown in the figure relevant distances are also
marked. T1 and T2 are the tensions in the
wires. By resolving in the horizontal and
vertical directions, write down equations
involving T1 and T2. Express these as one matrix
equation.
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2.
For the circuit given above, write down three
equations in terms of the three currents shown,
and then express these in one matrix equation.
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3.
A 40N weight mass is on a plane whose coefficient
of friction is 0.5, and the forces affecting the
mass are shown. Friction and the force F parallel
to the plane keep the mass in place. R is the
force applied by the mass normal to the plane, so
the frictional force is 0.5R. The force up the
plane is thus F 0.5R. By resolving forces
horizontally and vertically, write down equations
relating F and R and then express these equations
as one matrix equation. Note cos(36.87) 0.8
and sin(36.87) 0.6.
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4.
A mass (weight 2N) is suspended by three wires,
as shown above. Let the tensions in the wires be
T1, T2 and T3. The components of the tensions in
the x, y and z directions are For T1 -0.2T1,
0.5T1 and -0.1T1. For T2 0, 0.7T2 and
0.5T2. For T3 0.8T3, -0.7T3 and
-0.1T3. Express this system as a matrix equation.
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5.
Evaluate the following if they can be evaluated -
if not explain why. a) A B b) A B c) A
E d) A - 2B e) 5 C f) C D g) A E h)
F C i) DT C j) D A k) BT AT l)
B A m) FT C
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6.
Show that, even though C is not the zero matrix,
A.C B.C and yet A does not equal B.
7.
Show that A.AT is a symmetrix matrix.
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Answers
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c) Not the same size.
h) Incompatible sizes.
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