## 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

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