6. Consider the following matrices: A 2 6 21 = -3 -80 b = ' 4 9 223 [3. a) Perform a LU-decomposition on A. b) Use the LU-decomposition from A to solve Ax = b.

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Q: a) 9. Let F be an algebraically closed field, i.e. such that every polynomial with coefficients in F…

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Q: Prove that for all positive integers n, the number (27) is even. (Hint: Use Pascal's Identity.)

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Q: 6. Consider the complete graph Kn for n ≥ 3. Color r of the vertices in Kn red and theremaining n −…

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A: Since p∈P1​, it implies that p is a polynomial of degree at most one.Therefore, let p(x)=ax+b where…

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A: Step 1: Step 2: Step 3: Step 4:

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A: (b) Proving Mat<sub>2</sub>(ℕ) ≈ ℕTo show that the set of 2x2 matrices with natural…

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A: Part (a):   Part (b):   Part (c):    So eigenvalues are 0 and 2.

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A: Step 1: MatricesGiven matrices are:A=⎣⎢⎡​03−8​25−16​13−9​⎦⎥⎤​,B=⎣⎢⎡​−100​0−3−1​020​⎦⎥⎤​. Step 2:…

Q: Use Huffman coding to encode these symbols with given frequencies: A: 0.10, B: 0.25, C: 0.05, D:…

A: First, we arrange the symbols in increasing order of their frequencies. This gives us:C: 0.05, F:…