Prove that the set R ={ a+ b√2+c√3+d√6 , a,b,c,d belongs to Q } is a...

Prove that the set R ={ a+ b√2+c√3+d√6 , a,b,c,d belongs to Q } is a field

Expert Solution

Colby Messinger answered 2 years ago

Show that the set of all real numbers of the form a+b sqrt(2)+c sqrt(3)+d sqrt(6),where a,b,c,d...

Show that the set of all real numbers of the form a+b sqrt(2)+c sqrt(3)+d sqrt(6),where a,b,c,d ∈Q, forms a subfield of R

Find the value of a : b : c : d, if a : b = 2 : 3, b : c = 4 : 5 and c : d = 6 : 7.

1. Evaluate: (a+b)/(c-d) + 9/(a+d) when a=5, b=3, c=8, d=4 a. 6 b. 3 c. 15/2...

1. Evaluate: (a+b)/(c-d) + 9/(a+d) when a=5, b=3, c=8, d=4 a. 6 b. 3 c. 15/2 d. 17/13 2. Solve for x: 5(x+3) = 35 a. 2 b. 7 c. 4 d. -4 3. Acid rain occurs primarily as a result of a. operating a nuclear power plant b. burning coal or oil containing sulfur c. by-products created by operating an oil refinery d. the use of Freon and other refrigerants 4. The "ozone holes" at the polar region arise...

a. Prove that y=sin(x) is a subspace of R^2 b. Prove that a set of 2x2...

a. Prove that y=sin(x) is a subspace of R^2 b. Prove that a set of 2x2 non invertible matrices a subspace of all 2x2 matrices

Work out the products of the matrices E, R, R^2,R^3, A, B, C, D, and verify...

Work out the products of the matrices E, R, R^2,R^3, A, B, C, D, and verify that these products reproduce the multiplication table for the symmetries of the square, as expected. (Instead of computing all 64 products, compute “sufficiently many” products, and show that your computations suffice to determine all other products.)

let Q(sqrt(2),sqrt(3)) be the field generated by elements of the form a+bsqrt(2)+csqrt(3)+dsqrt(6) where a,b,c,d are in...

let Q(sqrt(2),sqrt(3)) be the field generated by elements of the form a+bsqrt(2)+csqrt(3)+dsqrt(6) where a,b,c,d are in Q(sqrt(2),sqrt(3)) is a vector space of dimension 4 over A. find a basis for Q(sqrt(2),sqrt(3))

Question

Prove that the set R ={ a+ b√2+c√3+d√6 , a,b,c,d belongs to Q } is a...

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Show that the set of all real numbers of the form a+b sqrt(2)+c sqrt(3)+d sqrt(6),where a,b,c,d...

Find the value of a : b : c : d, if a : b = 2 : 3, b : c = 4 : 5 and c : d = 6 : 7.

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