Below is a proof of Theorem 4.1.1 (b): For the zero vector ⃗0 in any vector...

Below is a proof of Theorem 4.1.1 (b): For the zero vector ⃗0 in any vector space V and k ∈ R, k⃗0 = ⃗0.

Justify for each of the eight steps why it is true.
1. k⃗0+k⃗0=k(⃗0+⃗0)
2. = k ⃗0
3. k⃗0 is in V
4. and therefore −(k⃗0) is in V .
5. It follows that (k⃗0 + k⃗0) + (−k⃗0) = (k⃗0) + (−k⃗0)
6. and thus k⃗0 + (k⃗0 + (−k⃗0)) = (k⃗0) + (−k⃗0).
7. We conclude that k⃗0 + ⃗0 = ⃗0
8. and so k⃗0 = ⃗0, as desired.

Expert Solution

Colby Messinger answered 2 years ago

1. Vector u =< 0,−1,3 > is given. Find a non zero vector v which is...

1. Vector u =< 0,−1,3 > is given. Find a non zero vector v which is perpendicular to u. Then ﬁnd a vector w which is perpendicular to both u and v. Explain the reason for your selection clearly. 2. Find the slope of the tangent line to the parametric curve x = 5 + sin(3θ) and y = −3 + 2tanθ at θ = π.

Theorem 3.4. Let a and b be integers, not both zero, and suppose that b =...

Theorem 3.4. Let a and b be integers, not both zero, and suppose that b = aq + r for some integers q and r. Then gcd(b, a) = gcd(a, r). a) Suppose that for some integer k > d, k | a and k | r. Show that k | b also. Deduce that k is a common divisor of b and a. b) Explain how part (a) contradicts the assumption that d = gcd(b, a).

Any amounts that should be blank must have a zero (0)!For each employee listed below,...

Any amounts that should be blank must have a zero (0)!For each employee listed below, determine the employer’s tax liability for the payroll period, as well as the totals for each employee and for each tax. Use the following tax rates.Social Security, 6.2%, with a maximum taxable earnings of $118,500.Medicare, 1.45%, with no cut-off.State Unemployment, 5.4%, with a maximum taxable earnings of 7,000.Federal Unemployment, .6%, with a maximum taxable earnings of 7,000.Name BeginningCumul-ativeCurrentPay EndingCumul-ativeAmount of TaxTotal Taxes on EmployerSoc. Sec.TaxesMedi-careTaxesSUTATaxesFUTATaxesAlice116,9002,300Bob48,0002,000Cindy6,8001,080Dale127,8001,580

Casey’s theorem proof step by step

Explain the Riemann series theorem proof.

proof of pappus' centroid theorem ( Volume)

Present Herglotz's theorem and its proof.

Write the proof of the dual Pappus theorem.

In the proof of Theorem 4.7 (Euclid’s proof that there are infinitely many primes), the argument...

In the proof of Theorem 4.7 (Euclid’s proof that there are infinitely many primes), the argument uses calculation of a number N. In each case below, suppose for the sake of demonstrating a contradiction, that the given list is the entire list of prime numbers. Calculate N and then factor N into primes to see that you do get a contradiction. (a) 2, 3, 5, 7, 11 (b) 2, 3, 5, 7, 11, 13, 17, 19 (c) 2, 3, 5,...

proof of the general stokes theorem using the greens and divergence theorem that is understandable by...

proof of the general stokes theorem using the greens and divergence theorem that is understandable by a calculus student

Question