Computer Vision - Week 0 Quiz Solutions

Question 1

Consider the following system of linear equations. 2x + 7y + 3z + w = 6 3x + 5y + 2z + 2w = 4 9x + 4y + z + 7w = 2 By solving the above mentioned system of linear equations, mention the number of free variables in the provided space below.

Correct Answer: 2

Question 2

Find out the eigen values of a matrix A=[-2112-3] and their corresponding eigen vectors

A.−1, −2 and k 1 (1/3, −1), k 2 (−1/4, −1) respectively. k 1 , and k 2 are two constants for free variables

B.1, −6 and k 1 (1/3, 1), k 2 (−1/4, 1) respectively. k 1 , and k 2 are two constants for free variables

C.1, 6 and k 1 (−1/3, 1), k 2 (−1/4, 1) respectively. k 1 , and k 2 are two constants for free variables

D.−1, 6 and k 1 (−1/3, −1), k 2 (−1/4, −1) respectively. k 1 , and k 2 are two constants for free variables

Correct Answer: 1, −6 and k 1 (1/3, 1), k 2 (−1/4, 1) respectively. k 1 , and k 2 are two constants for free variables

Question 3

Consider the data given below. v1=1-1-2, v2=5-4-7, v3=-310, y=-43h Which of the following options can be a value for h so that y lies in .

A.5

B.-5

C.-8

D.8

Correct Answer: 5

Question 4

Choose the correct options from the following.

A.The set of vectors [ 4 1 - 2 ] , [ - 3 0 1 ] , [ 1 - 2 1 ] are linearly dependent

B.The set of vectors [ 2 5 3 ] , [ 1 1 1 ] , [ 4 - 2 0 ] are linearly independent

C.Any set of vectors from R n that contains the zero vector is dependent

D.Any set of vectors from R n that contains the zero vector is independent

Correct Answers: The set of vectors [ 4 1 - 2 ] , [ - 3 0 1 ] , [ 1 - 2 1 ] are linearly dependent, The set of vectors [ 2 5 3 ] , [ 1 1 1 ] , [ 4 - 2 0 ] are linearly independent, Any set of vectors from R n that contains the zero vector is dependent

Question 5

Compute A10 given that A = PDP−1, where A=31-20, P=11-1-2, D=2101

A.[ 2047 1023 - 2 046 - 1 0 22 ]

B.[ 2046 1023 - 2 047 - 1 0 22 ]

C.[ 2047 1024 - 2 046 - 1 0 26 ]

D.[ 2048 1023 - 2 042 - 1 0 21 ]

Correct Answer: [ 2047 1023 - 2 046 - 1 0 22 ]

Question 6

Consider the following vectors, and compute the orthogonal projection of y onto u. y=76, u=42

A.[ 8 4 ]

B.[ - 8 4 ]

C.[ 8 -4 ]

D.[ -8 -4 ]

Correct Answer: [ 8 4 ]

Question 7

A single die is rolled once. Assume that the die is fair. Find the probability that the result of the roll is a number less than two and even.

A.0.1

B.0.01

C.0

D.0.001

Correct Answer: 0

Question 8

Consider Z as a standard normal random variable, then another normal random variable X = σZ + µ can be expressed as

A.X ∼ N(µ/2, σ2/2)

B.X ∼ N(µ, σ2/2)

C.X ∼ N(µ/2, σ2)

D.X ∼ N(µ, σ2)

Correct Answer: X ∼ N(µ, σ2)

Question 9

Which of the following are the properties of a Poisson experiment?

A.The experiment results in outcomes that can be classified as successes or failures

B.The probability that a success will occur is proportional to the size of the region

C.The probability that a success will occur in an extremely small region is virtually zero

D.The average number of successes (µ) that occurs in a specified region is unknown

Correct Answers: The experiment results in outcomes that can be classified as successes or failures, The probability that a success will occur is proportional to the size of the region, The probability that a success will occur in an extremely small region is virtually zero

Practice: Week 0 : Assignment 0