Engineering Mathematics: Nuclear Quiz 1

Find the rank of matrix

A matrix has eigen values are –2 and +2 and corresponding eigen vector are  and  then the matrix is

If for the given equations x + 2y – 3y = 1, (K + 2)z = 3, (2K + 1)y + 3 = 2 are inconsistent then the value of K is

 is equal to

The value of x for which the function is NOT continuous are

If f(1) = 1, f’(1) = 2, then

is ____.

The unit normal to the surface  at the point (2, 1, – 1) is

If u = log (x³ + y³ + z³ – 3xyz), the value of

The vector field (where and are unit vector) is