List of top Geo Engineering and Geo Informatics Questions on Linear Algebra

The value of \[ \int_{0}^{2+i}\left(\frac{\bar z}{2}\right)^2dz \] along \(x=2y\), is
Residue of \(\tan z\) at \(z=\dfrac{\pi}{2}\) is
Consider the function \[ f(x,y)=(x-2)^2(y+3). \] Then

The rank of the matrix \[ A= \begin{pmatrix} 1&2&3\\ 2&1&0\\ 0&1&2 \end{pmatrix} \]is

The eigen values of a \(3\times3\) real matrix \(A\) are \(1,-2,3\). Then
The value of the definite integral \[ \int_{0}^{1}\frac{xe^{x}}{(x+1)^2}\,dx \] is equal to
The value of the constant \(a\) so that the vector \[ \vec{V}=(x+3y)\hat{i}+(y-2z)\hat{j}+(x+az)\hat{k} \] is solenoidal is
Let \[ I=\int_C z\,dx+y\,dy+xz\,dz, \] where \(x,y,z\) are real and \(C\) is the straight line segment from the point \((0,2,1)\) to the point \((4,1,-1)\). The value of the line integral \(I\) is
Consider the function \[ f(x,y)=(x-2)^2(y+3). \] Then
The eigen values of a \(3\times3\) real matrix \(A\) are \(1,-2,3\). Then
The value of the definite integral \[ \int_{0}^{1}\frac{xe^{x}}{(x+1)^2}\,dx \] is equal to
The value of the constant \(a\) so that the vector \[ \vec{V}=(x+3y)\hat{i}+(y-2z)\hat{j}+(x+az)\hat{k} \] is solenoidal is
Let \[ I=\int_C z\,dx+y\,dy+xz\,dz, \] where \(x,y,z\) are real and \(C\) is the straight line segment from the point \((0,2,1)\) to the point \((4,1,-1)\). The value of the line integral \(I\) is
The value of \[ \int_{0}^{2+i}\left(\frac{\bar z}{2}\right)^2dz \] along \(x=2y\), is
Residue of \(\tan z\) at \(z=\dfrac{\pi}{2}\) is

The rank of the matrix \[ A= \begin{pmatrix} 1&2&3\\ 2&1&0\\ 0&1&2 \end{pmatrix} \]is