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This mock test of Linear Transform MCQ - 4 for Mathematics helps you for every Mathematics entrance exam.
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QUESTION: 1

Which one of the following is an eigenvector of the matrix

Solution:

So option (a) only satisfys the condition

QUESTION: 2

Suppose (λ_{1}X) be an eigen pair consisting of an eigenvalue and its correx eigenvector for a real matrix |λI - A| = λ^{3} + 3λ^{2} + 4λ + 3. Let I be a (n x n) unit matrix, which one of the following statement is not correct?

Solution:

QUESTION: 3

An eigenvector of

Solution:

QUESTION: 4

The eigenvalues of the matrix

Solution:

QUESTION: 5

For the matrix one of the eigenvalues is 3. The other two eigenvalues are

Solution:

QUESTION: 6

The characteristic vector of the matrix corresponding to characteristic root 1 is

Solution:

QUESTION: 7

The eigenvalues of a skew symmetric matrix are

Solution:

QUESTION: 8

The minimal polynomial m(x) of A_{nxn} each of whose element is 1 is

Solution:

QUESTION: 9

The characteristic equation of a 3 x 3 matrix A is defined as C(λ) = |λ - Al| = λ^{3} + λ^{2} + 2λ + 1 = 0. If l denotes identity matrix then the inverse of matrix A will be

Solution:

QUESTION: 10

Let A be area 4 x 4 matrix with characteristic polynomial C(x) = (x^{2} + 1)^{2} which of the following is true?

Solution:

QUESTION: 11

If A is 3 x 3 matrix over α, β, α ≠ β are the only characteristic roots (eigenvalues) of A in the characteristic polynomail of A is

Solution:

QUESTION: 12

If A is symmetric matrix λ_{1},λ_{2},.... ,λ_{n} be the eigenvalues of A and a_{11},a_{22},.....,a_{nn} is the diagonal entries of A. Then which of the following is correct?

Solution:

QUESTION: 13

The minimal polynomial of the 3 x 3 real matrix

Solution:

QUESTION: 14

A square matrix A is said to be idempotent if A^{2} = A. An idempotent matrix is non singular iff

Solution:

QUESTION: 15

be such that A has real eigenvalues then

Solution:

QUESTION: 16

then the eigenvalues of A are

Solution:

QUESTION: 17

Let A = [a_{jj}] be an n x n matrix with real entries such that the sum of all the entries in each row is zero. Consider the following statements

(I) A is non-singular

(II) A is singular

(III) 0 is an eigenvalue of A

Which of the following is correct?

Solution:

QUESTION: 18

The minimal polynomial m(A) of

Solution:

QUESTION: 19

Let A be a 2 x 2 real matrix of rank 1. If A is not diagonalizable then

Solution:

QUESTION: 20

are given vectors and A and if P = [x_{1} x_{2}] then P^{-1}AP

Solution:

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