M132: LINEAR ALGEBRA
Tutor Marked Assignment
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.
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.
c) If AB = 0, thenA = B = 0.
d) The vectors are linearly independent.
e) The vectors 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.
Tutor Marked Assignment
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.
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.
c) If AB = 0, thenA = B = 0.
d) The vectors are linearly independent.
e) The vectors 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.
