M132:
LINEAR ALGEBRA
Tutor Marked Assignment
M132 TMA Feedback Form
Q−1:[5×2 marks]
Answer each
of the following as True or False (justify your answer):
a)
If
m1 ≠m2 in the system 
, where m1
, m2 , b1 , and b2 are constants, then the
system has a unique solution.
, where m1
, m2 , b1 , and b2 are constants, then the
system has a unique solution.
b)
If
(c1 , c2) is a solution of the 2 x
2 system 
,
then, for any real number k, the ordered pair (kc1 , kc2)
is a solution.
,
then, for any real number k, the ordered pair (kc1 , kc2)
is a solution.
c) If AB = 0, thenA =
B =
0.
d)
The
vectors 
are
linearly independent.
are
linearly independent.
e)
The
vectors 
form
a linear combination with
.
form
a linear combination with.
Q−2: [1+3+2
marks]For the system:
a)
Write the coefficient
matrix A of the system
b)
Find det(A)
c)
Compute |-2A.AT.A-1|
Q−3:[1+4
marks]Consider
the linear system: 
a)
Write the augmented matrix for the system.
b)
Solve the system by applying the Gaussian
elimination method.
Q−4:[2+2+2 marks]Let
a) FindC(AT
+2B)
b) Find
BA - CD.
c) FindD2
-2C.
Q−5:[1
+ 2 + 2 marks]. Consider the linear
system: 
.
.
a) Write the
linear system in matrix form 
.
.
b) Find a
matrix C such that 
.
.
c) Find the
matrix B such that 
.
.
Q−6:[2+1+1
marks]Consider a linear system whose
augmented matrix is of the form:
. For
what values of a and b will the system have:
a) No Solution; b) A unique solution; c) Infinitely many solutions.
Q−7:[2+2+1 marks]Let A= 
.
.
a)
Find a
matrix B that is row equivalent to A.
b)
Determine
whether the fourth column vector forms a linear combination with the first three column vectors.
c)
Show that
the first three column vectors are linearly independent. Explain.
