STUPIDSID
If A =\(\begin{bmatrix} x & 4x\\ 2 & y \end{bmatrix}\\] \)has eigen values 5 and -1 then find values of x and y.
Evaluate \(\int_{c}(\bar{Z}+2z)dz\) along the circle c: \( x^{2}+y^{2}=1\)
Find dual of following LP model
max z= 2x1 +3x2+5x3
Subjected to
x1+x2-x3\(\ge\) -5
x1+x2+4x3=10
-6x1+7x2-9x3\(\le\)4
x1,x2\(\ge\)0 and x3 is unrestricted.
Using Cauchy's integral formula,evaluate \(\int_{c} \dfrac{(12z-7)dz}{(z-1)^{2}(2z+3)}\)where C: |z+i|=\(\sqrt{3}\\\)
Determine whether matrix a is derogatory A =\(\begin{bmatrix} 2 &1 &0 \\ 0&2 &1 \\ 0&0 &2 \end{bmatrix}\\\)
The daily consumption of electric power (in millions of kwh)is r.v with PDF f(x) =k xe-x/30 ,x>0.find k and the probability that on a given day the electricity consumption is more than expected electricity consumption.
Using Simplex method,solve the following LPP
max z = 15x1+6x2+ 9x3+2x4
s.t2x1+x2+5x3+6x4 \(\le\) 20
3x1 +x2+3x3+25x4\(\le\)24
7x1+x4\(\le\)70
& x1,x2,x3,x4\(\ge\) 0
Obtain ALL Taylor's and Laurent series expansion of function \(\dfrac{(z-1)(z+2)}{(z+1)(z+4)}about z=0\)
| Age of car(in years):x | 2 | 4 | 6 | 8 |
| maintenance cost :y (in thousands) | 5 | 7 | 8.5 | 11 |
Show that the matrix A is diagonalizable,Find its diagonal form and transforming matrix,if A =\(\begin{bmatrix} -9 &4 &4 \\ -8& 3 &4 \\ -16&8 &7 \end{bmatrix}\\\)
Using Cauchy's residue theorem,show that \(\int_{0}^{2\pi}\dfrac{cos 2\theta}{5+4cos\theta}d\theta=\dfrac{\pi}{6}\\\)
Using Dual simplex method,solve
max z = -2x1 -x3
s.t x1 +x2 -x3 \(\ge
\)5
x1 -2x2 +4x3 \(\ge\)8
& x1 ,x2 ,x3 \(\ge\) 0
Maximize Z=2x12 +12x1 x2-7x12
subject to the constraints 2x1 +5x2 ? 98 and x1 , x2 7 ? 0