M is a 2 × 2 matrix with eigen values 4 and 9. The eigen values of M<sup>2</sup> are

Let the eigen values of a 2 × 2 matrix A be 1, -2 with eigen vectors x₁ and x₂ respectively. Then the eigen values and eigen vectors of the matrix A² - 3A + 4$$I$$ would, respectively, be

A

2, 14; x₁, x₂

B

2, 14; x₁ + x₂, x₁ - x₂

C

2, 0; x₁, x₂

D

2, 0; x₁ + x₂, x₁ - x₂

Consider the following pattern of numbers: $\dfrac{\begin{matrix} 8 \\\ 6 \ \\\ 4 \ \end{matrix}}{ \ 6} \ \ \dfrac{\begin{matrix} 10 \\\ 5 \ \\\ 6 \ \end{matrix}}{ \ 11} \ \ \dfrac{\begin{matrix} 15 \\\ 7 \ \\\ 8 \ \end{matrix}}{ \ 16} \ \ \dfrac{\begin{matrix} 13 \\\ 4 \ \\\ 8 \ \end{matrix}}{ \ ?}$ What is the number at ? in the above pattern?

A

17

B

19

C

21

D

23

Consider the system of equations A_{(n × n)} X_{(n × 1)} = λ_{(n × 1)} where, λ is a scalar. Let (λ_i, x_i) be an eigen-pair of an eigen value and its corresponding eigen vector for real matrix A. Let $$I$$ be a(n × n) unit matrix. Which one of the following statement is NOT correct?

A

For a homogeneous n × n system of linear equations, (A - λ$$I$$)x = 0 having a nontrivial solution, the rank of (A - λ$$I$$) is less than n

B

For matrix A^m, m being a positive integer, (λ_i^m, x_i^m) will be the eigen-pair for all i

C

If A^T = A^-1, then |λ_i| = 1 for all i

D

If A^T = A, then λ_i is real for all i

A 3 × 3 matrix has elements such that its trace is 11 and its determinant is 36. The eigen values of the matrix are all known to be positive integers. The largest eigen value of the matrix is

A

18

B

12

C

9

D

6

The eigen values of a (2 × 2) matrix X are -2 and -3. The eigen values of the matrix (X + $$I$$) (X + 5$$I$$) are

A

-3, -4

B

-1, -2

C

-1, -3

D

-2, -4

Let us consider a square matrix A of order n with Eigen values of a, b, c then the Eigen values of the matrix AT could be.

A

a, b, c

B

-a, -b, -c

C

a-b, b-a, c-a

D

a-1, b-1, c-1

The Eigen values of a 3×3 matrix are λ1, λ2, λ3 then the Eigen values of a matrix A3 are __________

A

λ1, λ2, λ3

B

$ \frac{1}{λ_1}, \frac{1}{λ_2}, \frac{1}{λ_3}$

C

$λ_1^3, λ_2^3, λ_3^3$

D

1, 1, 1

Consider the following statements regarding homogenous coordinate transformation matrix: 1. A homogenous transformation matrix can be considered to consist of four sub-matrices. 2. The upper left 3 × 3 sub-matrix represents the position vector. 3. The upper right 3 × 1 sub-matrix represents the rotation matrix. 4. The lower left 1 × 3 sub-matrix represents perspective transformation. Which of the above statements are correct?

A

1 and 3

B

1 and 4

C

2 and 3

D

2 and 4

A real traceless 4 × 4 matrix has to eigen values -1 and +1. The other eigen values are

A

zero and +2

B

-1 and +1

C

zero and +1

D

+1 and +1

A word is represented by only a set of numbers as given in any one of the alternatives. The sets of numbers given in the alternatives are represented by two classes of alphabets as shown in the given two matrices. The columns and rows of Matrix-I are numbered alternatively and represented by two classes of alphabets as shown in the given two matrices. The columns and rows of Matrix-I are numbered from 0 to 4 and that of Matrix-II are numbered from 5 to 9. A letter from these matrices can be represented first by its row and next by its column, for example, ‘C’ can be represented by 42, 56 etc and ‘P’ can be represented by 03, 65 etc. Similarly, you have to identify the set for the word ‘THRONE’. Matrix I Matrix II 0 1 2 3 4 5 6 7 8 9 0 H D U P F 5 J C N R G 1 O S K X I 6 P V T X L 2 R E W A Z 7 E Y W A O 3 B T Q Y N 8 K H Q U I 4 J L C V G 9 B S F M D

A

67, 86, 20, 79, 34, 75

B

31, 00, 58, 79, 10, 34

C

67, 10, 75, 20, 58, 40

D

31, 10, 79, 86, 13, 75

M is a 2 × 2 matrix with eigen values 4 and 9. The eigen values of M² are

Related Questions

M is a 2 × 2 matrix with eigen values 4 and 9. The eigen values of M2 are

Related Questions

M is a 2 × 2 matrix with eigen values 4 and 9. The eigen values of M² are