Write the general form of discretization for the following boundary value problem y" = − 3y + 2y + 2x +3, 0 ≤ x ≤ 1, y(0) = 2, y(1) = 1, in matrix-vector notation Aw = b.
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- Show that the three points (x1,y1)(x2,y2) and (x3,y3) in the a plane are collinear if and only if the matrix [x1y11x2y21x3y31] has rank less than 3.Find the augmented matrices of th e linear systems x +5y = -1 , -x + y = -5 ,2x + 4y = 4Find the relative extrema of the following functions and determine their nature (maximum, minimum or chair point) Using the Hessian matrix criterion. Please explain step by step and be specific. b) f(x, y) = x3 + 3xy2 − 15x − 12y. j ) f(x, y) = ex−y(x2 − 2y2).
- Suppose that f(x,y)∈C^2 in some neighborhood of (a,b) and that fx(a,b)=0=fy(a,b). If the Hessian matrix of f is (3−3−3−5) at a critical point (a,b), then (a,b) is a saddle point local minimum local maximum degenerate critical pointFind the relative extrema of the following functions and determine their nature (maximum, minimum or chair point) Using the Hessian matrix criterion. Please explain step by step and be specific. j ) f(x, y) = ex−y(x2 − 2y2).Minimize ƒ(x, y, z) = xy + yz subject x2 + y2 - 2 = 0 and x2 + z2 - 2 = 0.
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- Show that the volume of a triclinic unit cell of sides a, b, and c and angles α, β, and γ is V = abc(1 − cos2α − cos2β − cos2γ + 2 cos α cos β cos γ)1/2 . There is this answered question already over here, but I have a dout regarding the process it took to get to the result, specifically, once we have our 3x3 matrix, how do we determine that this matrix equals to the linear eq? this is the image :DCompute ƒxz and ƒzz for ƒ(x, y, z) = xyz - x2 z + yz2.A = (ai j )is a 3 × 3 matrix, develop the general ex-pression for det(A) by expanding(a) along the second column;(b) along the third row.