Show that it is impossible to find a basis for the vector space ofn x n (n > 1) matrices such that each pair of elements in the basiscommutes under multiplication.

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A: Given g(x, y) = x² + y² + x²y on the circle x² + y² = 12 using the method of Lagrange multipliers.

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Q: Provide a direct proof for the argument. For every real numbers b and c, c≠0, |b/c|=|b|/|c|.

A: Please see the attachment

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Q: for $61,000, including taxes and license fees. You saved $13,000 for a down payment. The dealer is…

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Q: II. Determine whether the given is rational equation, rational inequality, rational function, or…

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Q: I. Evaluate S x² +6 x³ + 3x dx.

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Q: Prove or disprove that Q(√3) and Q(√-3) are ring-isomorphic.

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Q: A 3x3 matrix has three eigenvalues -3, -2 and 1. Its characteristic equation is ... O Ap(2) = 2³+42²…

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Q: Let W = {(x1, x2, x3) = R³ : x₁ + 2x2 − 3x3 = 0} x1 (a) Find a basis of W. (b) Give an example of a…

A: Answer follows

Q: Let B be a subset of a vector space V. Show that B is a basis for V ifand only if every member of V…

A: Basis: A basis is a set of vectors such that the vectors are linearly independent and these vectors…

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A: Let us solve the given LPP problem with the help of Simplex method in the next steps.

Q: 3x 5y-2z 3) f(x, y, z)= tan-1. (-10, 0, 0) 4) f(x, y, z) - In(x2 + 4y2 + 3z2), (4,4,4)

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Q: 3. Let f(x) = e = sin(x) + x - 1. To evaluate f(x) near zero we need to compare f(x) to the Taylor…

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Q: 11-12 Sketch the graph of the function and use it to determine the values of a for which limx→a f(x)…

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Q: Problem 6. Explain why the coefficient of x'y the same as the coefficient of x'y in the expansion of…

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Q: When demonstrating that lim (2x + 3) = 7 with ε = 0.2, which of the following d-values suffices? x →…

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Q: Prove Cantor's Theorem (Revised) For all A, |A| < |p(A)|. |p(A)| - power set of A

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Q: 7 Let a and b be vectors in R" such that ||a||=||b||=2 and (a,b) = 1. Then ||ab||= ...

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Q: [ 3x - 8x+1 (x−4)(x + 1) dx [Use partial fraction:

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Q: O Determine the x-values for which the given graph is increasing and decreasing. a. Increasing:…

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Q: . Let consider f(x) = x³-3x on the interval [-1,2]. (a) Execute first 2 iterations of Golden Section…

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Q: 1. Sketch the graphs of the following combinations of step functions: (a) H(t)- H(t-3) (b) 2H(t-1) +…

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.