(1/2)^{2}

^{10 }C_{2}(1/2)

(1/2)^{10}

^{10 }C_{2}(1/2)^{10}

Number of elements in sample space is 2

We have

where p and q are arbitrary real numbers. Which of the following statements about the controllability of the system is true ?

The system is completely state controllable for any nonzero values of p and q

Since S is singular, system is completely uncontrollable for all values of p and q .

We have

By property of unilateral laplace transform

Sum of the principal diagonal element of matrix is equal to the sum of Eigen values. Sum of the diagonal element is -1 - 1 + 3 = 1.In only option (D), the sum of Eigen values is 1.

I. y1, y2 and y3 are linearly independent on -1 ≤ x ≤ 0

II. y1, y2 and y3 are linearly dependent on 0 ≤ x ≤ 1

III. y1, y2 and y3 are linearly independent on 0 ≤ x ≤ 1

IV. y1, y2 and y3 are linearly dependent on -1 ≤ x ≤ 0

Which one among the following is correct?

It is given that A has only one real eigen value. Then the real eigen value of A is