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GATE EE 2018 - Engineering Mathematics Daily Quiz- 2

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Question 1

Let the eigenvalues of a 2 x 2 matrix A be 1, -2 with eigenvectors

and

respectively. Then the eigenvalues and eigenvectors of the matrix

would, respectively, be

Question 2

The linear operation L(x) is defined by the cross product L(x) = B x X, where b = [0 1 0]^T and

are three dimensional vectors. The "3x3" matrix M of this operation satisfies

Then the eigenvalues of M are

Question 3

If R =

the top row of R^‒¹ is :

Question 4

For the set of equations,
x₁ + 2x₂ + x₃ + 4x₄ = 2 and
3x₁ + 6x₂ + 3x₂ + 12x₄ = 6
The following statement is true

Question 5

A is an m × n full rank matrix with m > n and I is an identity matrix. Let matrix A⁺ = (A^TA)^–1A^T. Then, which one of the following statements is FALSE?

Question 6

Cayley-Hamilton Theorem states that a square matrix satisfies its own characteristic equation.
Consider a matrix

. The relation satisfied by the matrix A is:

Question 7

The characteristic equation of a (3 × 3) matrix P is defined as a (l) = | lI – P | = l³ + l² + 2l + 1 = 0.
If I denote identity matrix, then the inverse of matrix P will be

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ESE & GATE EE Engineering Mathematics

Jul 15ESE & GATE EE