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for all x = (x1, x2), y = (y1, y2) ∈ V , α1, α2, β1, β2 some fixed real numbers, and scalar multiplication is the usual scalar multiplication. What values of α1 , α2 , β1 , β2 make V a vector space (over R).
Pay $40 for plan offered for $30 for plan what percentage of savings
Prove that the mapping a(g) = g^-1 for all g in G is an automorphism if and only if G is Abelian. An isomorphism from a group G onto itself is called an automorphism of G.
Examples of the product rule of exponents: Sometimes when students see the rule they want to write it as 4^2 + 4^3 = 4^5. Can you explain why this does not work?
Use de Moivre's formula to verify that the fifth roots of unity form a group under complex multiplication, showing all work. Prove that G is isomorphic to Z5 Let F be a field. Let S and T be subfields of F.
execute a strategy out when the supernova actually occures, relative to when the chinese astronomers saw the explosion
A new bone study is being planned that will measure the biomarker TRAP described in Exercise 6.17. Using the value of σ given there, 6.5 U/l, ?nd the sample size required to provide an estimate of the mean TRAP with a margin of error of 1.5 U/l fo..
Let H be the unbounded self-adjoint operator defined by -d^2/dx^2 (the negative of the second derivative with respect to x) on: D(H) ={f element of L^2 | Integral( |s^2 F f(s)|^2 )ds element of L^2}
Does multiplication of two imaginary numbers imaginary or real? if i multiply 2i and 3i then it is = -6 which is real .if √-3 and √-2 are multiplied then it gives - √6 which is real . but if i do the same thing like this √-3 * √-2 =√{(-3)*(-2)} =√6 w..
Are all linear equations functions? Is there an instance when a linear equation is not a function? Support your answer.
A ball drops from a height of 22 feet. Each time it hits the ground, it bounces up 70 percents of the height it fall. Assume it goes on forever, find the total distance it travels.
Find the derivatives of the following functions and please show all steps: (a) f(x) = (x-1)^3 . e^4^x (b) y = x^3 ln(x^2 +1)
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