Consider the example where G is the symmetries of the square, and H is the rotations of the square. Then the two cosets of H are { elt[1], elt[2], elt[3], elt[4] } = H = H xid, and { elt [5], elt [6], elt [7], elt [8] ] = H • elt [5]. A set of coset representatives is { elt[1], elt[5] } and the reader can verify that each element is uniquely expressible as a product of an element of H and a coset representative.

Q: 3. Find the ranks and nullities of the following linear maps T: U → V, and find bases of the kernel…

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Q: {(:}) (::). (; })· (; )} 1 1 1 2 2 3 3 4 2 2 3 4 5 1 7 3

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Q: :) The set B = {-(1 + x²), 3x − 4 − 4x², 7 - 6x + 6x²} is a basis for P₂. Find the coordinates of…

A: Let us consider the element v and B be the basis then,  To write the vector v in the linear…

Q: 2. Let A e Mat2×3(R) be as below: -1 3 7 A = 4 -3 2 Find a (row) echelon form of A. Write down bases…

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Q: Q1. Show that the first four Laguerre polynomials [named for the French mathematician Edmond…

A: The first four Laguerre polynomials are 1, 1 - x, 2 - 4x + x², 6 - 18x + 9x² - x³.

Q: Find the coefficient of x5 in (1 – 2x)-7 using generating function.

A: Given to find the coefficient of x5 in 1-2x-7 The generating function will be Gx=1-2x-7…

Q: Factor completely. qs - 8s + qf - 8f qs - 8s + qf - 8f =

A: We have to complete factor

Q: asis: The set B = {2-3x², 8+x-12x², 33x² - (21+ 2x)} is a basis for P₂. Find the coordinates of p(x)…

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Q: ?:R3 →R2,with? ?,?,? =(?+2?+3?,4?+?−2?) Find a basis for the image and state its dimension.

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Q: The set B = {2+ 2x², 4 − 3x + 4x², 19 − 9x + 18x²} is a basis for P₂. Find the coordinates of p(x) =…

A: Given Basis: B=2+2x2, 4-3x+4x2, 19-9x+18x2. To find: Find the coordinate of px=84-39x+80x2 relative…

Q: Let consider given points: (0, 1), (2,3), (3,0). (a) Use Lagrange interpolation to find a polynomial…

A: Note: “Since you have posted multiple questions, we will provide the solution only to the first…

Q: If GCD of (a,b) is 1 we can find the lcm by multiplying a and b. True or false

A: if GCD(a,b) is 1, We can find lcm by multiplying a and b.   This statement is True.

Q: 10 In each part, use the Lagrange interpolation formula to construct the polynomial of smallest…

A: Since you have posted a question with multiple sub parts. We will solve the first three sub parts…

Q: Find the standard inner product on P of the given polynomials. p= -2+ 4x + a2, q = 3+ 4x 3a2. (p, q)

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Q: R4 Span {v1,..., V4}. Explain why {v1,..., V4} Is a basis for 4

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Q: Find the largest z for which 2x + 4y = 5 and x2 + z2 = 2y.

A: Given- 2x+4y=5 and x2+z2=2y To find- The greatest vlue of z. Concept Used- To find the largest…

Optimization Models

Optimization models are mathematical models that help organizations determine the best way to allocate scarce resources to achieve specific objectives. These models can be used to solve a wide variety of problems, from finding the most efficient route for a delivery truck to determining the optimal mix of products to stock in a store.