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Question : How do you find UP PGT Math Question solution of the following Solution : Diameters of circle are the lines \[2x-3y\ =\ 5 \] (1) And \[ 3x-4y\…

Question : prove that (0,0), (1,-1),(-1,1) are solutions of the system of non linear equations equations given as \[x=y\left(1-\left(x^2+y^2\right)\right) , y=x\left(1-\left(x_2+y^2\right)\right) \] Solution : Given system of non linear equations…

Question : Find Jacobian of functions given below \[f(x,y)=y\left(1-\left(x^2+y^2\right)\right) , g(x,y)=x\left(1-\left(x_2+y^2\right)\right) \] Solution : given functions \[f(x,y)=y\left(1-\left(x^2+y^2\right)\right) , g(x,y)=x\left(1-\left(x_2+y^2\right)\right) \] Their first order partial derivatives are \frac{\partial f}{\partial x} =…

Question : Solve following system of non linear equations \[x=y\left(1-\left(x^2+y^2\right)\right) , y=x\left(1-\left(x_2+y^2\right)\right) \] Solution : \[x=y\left(1-\left(x^2+y^2\right)\right) \] (1) \[y=x\left(1-\left(x_2+y^2\right)\right) \] (2) From eqn (1) \[\frac{x}{y}=1-\left(x^2+y^2\right)\] From eqn (2) \[\frac{y}{x}=1-\left(x^2+y^2\right)\] Equating…

Introduction : We shall explain the process of how to convert polar equation to cartesian equation through solving following question. Question : The equation \[r\left(6-4\cos{\left(\theta\right)}\right)=5\] represents \[\] (A)a parabola (B)…

Question: Vectors x =(1,0,1) , y =(-4, a, 4) and z =(a, -1, -a) are linearly dependent in R^3, then value of a is equal to (A)2 (B) -2 (C)+2,…

Question : For what value of m the vector (m, 3, 1) is a linear combination of the vectors (3, 2, 1) and (2, 1,0) ? (A)2 (B) 3 (C)5…

Introduction : Here we shall explain the process of how to find dimension of vector space of solutions of a differential equation through step by step solution of the following…

Question : Find data plot matlab for the following cases (a) \[x_1=\left(\begin{matrix}0\\1\\2\\3\\4\\5\\6\\7\\8\\9\\10\\\end{matrix}\right),y_1=\left(\begin{matrix}1\\0.9\\0.8\\0.7\\0.6\\0.5\\0.4\\0.3\\0.2\\0.1\\0\\\end{matrix}\right)\ \ \] (b) \[x_2=(x_i), x_i = 2i, 0\le i \le 50 , y_2 =(e^{x(i)})\] Solution : (a) %program…

Question : Find analytical solution of ode \[y'+2y=e^(-4t)+cos(2pit)\] such that y(0)=1 Solution : Given differential equation\[y^\prime+2y=e^{-4t}+\cos{\left(2\pi t\right)},y\left(0\right)=1\] (1)This equation can be written in the form \[y^\prime+P\left(t\right)y=Q\left(t\right)\]Which is Linear ODE of…