The matrix is
is positive definite
is positive semi-definite
is not positive semi-definite
is negative semi-definite
Difficulty Level: 1
Positive Marks: 1.00
Negative Marks: 0.33

is positive definite
is negative definite
is negative semi-definite
None of the above
Difficulty Level: 1
Positive Marks: 1.00
Negative Marks: 0.33

Is indefinite
is definite
is negative semi-definite
None of the above
Difficulty Level: 1
Positive Marks: 1.00
Negative Marks: 0.33

The pair of linear equations kx + 2y = 5 and 3x + y = 1 has a unique solution if

Choose the correct options: [MSQ]

k = 1

k ≠ 6

k =0

K = 1

Difficulty Level: 1
Positive Marks: 1.00
Negative Marks: 0.00
Solve the system of equations

x + y + z = 9

2x - 3y + 4z = 13

3x + 4y + 5z = 40

Choose the correct options: [MSQ]

x = 0, y = 3
x = 1, z = 5
y = 3, z = 5
z = 2, x = 4
Difficulty Level: 1
Positive Marks: 1.00
Negative Marks: 0.00
The following quadratic form

is positive definite
is negative definite
is negative semi-definite
None of the above
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.66
The eigenvalues of are

2, 4, 7
-2, -5, 7
-2, -2, 7
2, 3, 6
Difficulty Level: 1
Positive Marks: 1.00
Negative Marks: 0.66
The solution of the system of equations 3x + 2y - 6z = 1, 2x - 3y + 3z = -1, x - 4y + z = -6 is:
(1, -2, 1)
(1, 1, 2)
(2, 1, 1)
(1, 2, 1)
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.66
In the solution of the following set of linear equation by Gauss elimination using partial pivoting the pivots for the elimination of x and y are _______ respectively

x + 4y – z = -5

x + y – 6z = -12

3x – y – z = 4

3
13/3
5/3
13/4
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.66
Let 𝐴 be a 3 × 3 real matrix with det(𝐴 + 𝑖 𝐼) = 0, where 𝑖 = √−1 and 𝐼 is the 3 × 3 identity matrix. If det(𝐴) = 3, then the trace of A^2 is __________
7
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.00
Let the Eigenvector of the matrix be written in the form . What is the value of

(a + b)?

0.5
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.00
The set of equations

x + y + z = 1

ax – ay + 3z = 5

5x – 3y + az = 6 has infinite solutions, if a =

4
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.00
If is an eigenvector of , the eigenvalue corresponding to the eigenvector is

4
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.00
One of the Eigen vectors of the matrix

Choose the correct options: [MSQ]

Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.00
The eigenvalues of are
5
37
19
-19
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.00