Description

Quiz – 3

Group 1
(One among the following set of questions)
1. (3 points) Consider a matrix A ∈R4×4 given by
 
1 a 0 0
 
 0 1 b 0 
A =   (1)  
 0 0 1 c 
   
0 0 0 1
Let B ∈ R4×4 denote the inverse of a matrix. Compute the entry B13 [Hint: use the idea of inverse linear
transformation].
2. (3 points) Consider a matrix A ∈R4×4 given by
 
1 a 0 0
 
 0 1 b 0 
A =   (5)  
 0 0 1 c 
 
 
0 0 0 1
Let B ∈ R4×4 denote the inverse of a matrix. Compute the entry B14 [Hint: use the idea of inverse linear
transformation].
Group 2
(One among the following set of questions)
1. (1 point) If ∀v ∈Rn Av = Bv (where A ), then A = B.
A. True
B. False
2. (1 point) If ∃v ∈Rn such that Av = Bv (where A ), then A = B.
A. True B. False
Group 3 (All the questions)
1. (2 points) Consider a matrix A ∈R4×4 whose column vectors are given by
a1 =e1
a2 =e3 + xe2
(9)
a3 =xe3−e2 a4 =e4
The rank of the matrix is
2. (2 points) Consider a matrix A ∈R4×4 whose column vectors are given by
a1 =e1
a2 =e3 + xe2
(10)
a3 =xe3−e2 a4 =e4
The nullity of the matrix is
3. (4 points) Consider a matrix A ∈R4×4 whose column vectors are given by
a1 =e1
a2 =e3 + xe2
(11)
a3 =xe3−e2 a4 =e4
The second entry of the vector x such that Ax = b (where b = [p,q,r,s]t is 4. (4 points) Consider a matrix A ∈R4×4 whose column vectors are given by
a1 =e1
a2 =e3 + xe2
(14)
a3 =xe3−e2 a4 =e4
Let C = ATA. The entry C2,2 is
5. (4 points) Consider a matrix A ∈R4×4 whose column vectors are given by
a1 =e1
a2 =e3 + xe2
(16)
a3 =xe3−e2 a4 =e4
Let C be the inverse of A. The entry C2,2 is