Linear Algebra

Question 51

Find the boolean product A⊙B of the two matrices.

• (1)

• (2)

• (3)

• (4)

Question 52

If C is a skew-symmetric matrix of order n and X is n x 1 column matrix, then X^TCX is a

• scalar matrix
• null matrix
• unit matrix
• matrix will all elements 1

Question 53

In a compact one dimensional array representation for lower triangular matrix (all elements above diagonal are zero) of size n x n, non zero elements of each row are stored one after another, starting from first row, the index of (i, j)^th element in this new representation is

• i+j
• j+i(i-1)/2
• i+j-1
• i+j(j-1)/2

Question 54

A 4×4 DFT matrix is given by : (j² = −1) Where values of x and y are _____, _____ respectively.

• 1, −1
• −1, 1
• −j, j
• j, −j

Question 55

If A is a skew symmetric matrix, then A^t

• diagonal matrix
• A
• -A
• 0

Question 56

Let R and S be two fuzzy relations defined as : Then, the resulting relation, T, which relates elements of universe x to the elements of universe z using max-min composition is given by :

• (1)
• (2)
• (3)
• (4)

Question 57

A neuron with 3 inputs has the weight vector [0.2 –0.1 0.1]^T and a bias θ = 0. If the input vector is X = [0.2 0.4 0.2]^T then the total input to the neuron is :

• 0.20
• 1.0
• 0.02
• –1.0

Question 58

Which of the following is used to determine the specificity of requirements? (1) n₁ / n₂ (2) n₂ / n₁ (3) n₁ + n₂ (4) n₁ - n₂ Where n₁ is the number of requirements for which all reviewers have identical interpretations, n₂ is number of requirements in a specification.

• (1)
• (2)
• (3)
• (4)

Question 59

Consider the Breshenham’s line generation algorithm for a line with gradient greater than one, current point (x_i, y_i) and decision parameter, d_i. The next point to be plotted (x_i+1, y_i+1) and updated decision parameter, d_i+1, for d_i < 0 are given as _______.

• x_i+1 = x_i +1 y_i+1 = y_i d_i+1 = di_i+ 2 dy
• x_i+1 = x_i y_i+1 = y_i +1 d_i+1 = di_i+ 2 dx
• x_i+1 = x_i y_i+1 = y_i +1 d_i+1 = d_i+ 2 (dx -dy)
• x_i+1 = x_i +1 y_i+1 = y_i +1 d_i+1 = d_i+ 2 (dx -dy)

Question 60

Consider the problem of a chain < A₁, A₂, A₃, A₄> of four matrices. Suppose that the dimensions of the matrices A₁, A₂, A₃ and A₄ are 30 × 35, 35 × 15, 15 × 5 and 5 × 10 respectively. The minimum number of scalar multiplications needed to compute the product A₁A₂A₃A₄ is ____.

• 14875
• 21000
• 9375
• 11875