Engg.Mathematics II

 Find the Eigen values for the following 2×2 matrix.  $A=\left|\frac{1}{2}\frac{8}{1}\right|$  

• -3

• 2

• 6

• 4

The sum of the eigen values of a matrix is the sum of the elements of the

• principal diagonal

• diagonal element

• equal

A square matrix A and its transpose have the same

• Eigen vectors

• Eigen values

• same values

Use of cayley hamilton theorem

• +ve integral powers of A , invers of a non singular square matrix

• -ve integral powers of A , invers of a non singular square matrix

• +ve integral powers of A , invers of a singular square matrix

Find the nature of  $2x_1x_2+2x_1x_3-2x_2x_3$  

• Definite 

• semi definite

• indefinite 

 $Find\ rank\ and\ signature\ 2x_1x_2+2x_1x_3+2x_2x_3$  

• 3,1

• 3,-1

• 2,1

• 2,-1

A vector field which has a vanishing divergence is called as ____________

• Solenoidal field

• Rotational field

• Hemispheroidal field

• Irrotational field

A vector field with a vanishing curl is called as __________

• a) Irrotational

• b) Solenoidal

• c) Rotational

• d) Cycloidal

 $find\ \nabla r$  

•  $\frac{\overrightarrow{r}}{r}$  

•  $\frac{r}{\overrightarrow{r}}$  

•  $\overrightarrow{r}$  

•  $r$  

 $if\ \nabla\phi=2xy\overrightarrow{i}+x^2z\overrightarrow{j}+x^2y\overrightarrow{k},\ find\ \phi$  

• xyz

•  $x^2yz$  

•  $xy^2z$  

•  $xyz^2$