Question No. 1: Part:a: For matrix -1 4 - 2] A = -3 4 | -3 1 3 Calculate all eigenvalues and eigenvectors of A. Compute A4 by diagonalizing A into PDP-1.

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Q: Let F : R" → R™ and g : R" → R. Prove that d(gF)[a; h] = g(a)dF[a; h] + F(a)dg[a; h].

A: let the functions be  F:ℝn→ℝm , g:ℝn→ℝ prove that  dgFa;h=gadF[a;h]+F(a)dg[a;h]

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Q: 5.13 A square matrix is a matrix that has an equal number of rows and columns. In mathematics, m x m...

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Q: Let a = and b =. Show that there are scalars s and t so that sa + tb =. You might want to sketch the...

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A: Here volume of the prism will be V=lbh So the change in volume in time t will be given by dvdt=lbdhd...

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A: A function f(x) is continuous at a point x=a if  fa-0=fa+0=fa  

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Q: Q2. Use Newton the forward-difference formula to construct interpolating polynomials of degree one, ...

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Q: Factor P(x) = x^4 + x^3 + x^2 + x. * O x(x + 1)(x^2 + 1) O (x - 1)(x^2 + 1) O (x + 1)(x^2 + 1) O x(x...

A: Use the reaminder theorem to factor the given polynomial as in next.

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Q: Prove that n/n2 +1 is greater than (n+1)/ (n+1)2 + 1

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Q: (b) Define subspace and Verify whether is subspace v = {(x,y,2):x,y,2ER² and x-2y+3z = 5}

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Q: Ex. 54 Show that the following additive group is cyclic and give its generator. 1. H2 the set of all...

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Q: f (x) = 5e0.5x at X = 2, find the relative approximate error using value 1. Given from h = 0.25 and ...

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