21. Find a zero divisor, if possible, in each of the following. If not possible, explain...
Definition A: Let R be ring and r e R. Then r is called a zero-divisor in Rifr+0r and there exists SER with s # OR and rs = OR. Exercise 1. Let R be a ring with identity and f € R[2]. Prove or give a counter example: (a) If f is a zero-divisor in R[x], then lead(f) is a zero-divisor in R. (b) If lead(f) is a zero- divisor in R[x], then f is a zero-divisor in R[2]....
3. Is each of the following is a subspace of R4? If yes, find a basis A. The set of all (x1, z2, s, z4) that satisfy both 2x1-32 o 51 +22 30 B. The set of all (x1,22, z3, z4) that satisfy both 5x1+22 3 0 3. Is each of the following is a subspace of R4? If yes, find a basis A. The set of all (x1, z2, s, z4) that satisfy both 2x1-32 o 51 +22 30...
Please explain how to find this answer. 21. Determine the wavelength of each wave. Assume each wave is traveling at 3.00 X 108 m/s. a. a wave with a frequency of 750,000 s-1 b. a wave with a frequency of 20 Hz c. a wave with a frequency of 2.5 X 105 Hz
21. Find the derivative of each of the following functions by applying the product rule a. f(x) = (x2 + 1][2x2 + 3x + 4) b. f(x) = x2 cos x c. f(x) = e* sin x 22. Find Find the derivative of each of the following functions by applying the quotient rule a. f(x) = 22+1 f(x) = (2x + 1] / [x - 3] b. f(x) = x+2x+1 3x + 1 c. f(x) = sing 23. Find the...
#3 J. Properties of Divisors of Zero Prove that each of the following is true in a nontrivial ring. 1 If a ±1 and a2= 1, then a + 1 and a-1 are divisors of zero . # 2 If ab is a divisor of zero, then a or b is a divisor of zero. In a commutative ring with unity, a divisor of zero cannot be invertible.
is it possible for an object to have zero velocity but non-zero acceleration? If so, give an example from your experiments. In any case, explain why. A motion diagram might help.
Find the zeros for the given polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around at each zero fix)=x2-8x? + + 16x Determine the zero(s). If they exist. The zero(s) is/are D (Type integers or decimals. Use a comma to separate answers as needed) Find the zeros for the given polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis...
21. Indicate whether each of the statements is T or F. Explain the reason. (12 pts) c) Vm E Z*,n E Z4 [n |m ^ gcd(m,n) 1] _ 21. Indicate whether each of the statements is T or F. Explain the reason. (12 pts) c) Vm E Z*,n E Z4 [n |m ^ gcd(m,n) 1] _
Please explain as detailed as possible, thank you! 1. Let S={0, 1, 2, 3, . . . , 150). and let A={x E S | x+100 E S} Write the roster notation of the set A. Also, find the cardinality of the set A. 2. For each natural number n, let An be the interval An (0,2/n) and let Bn be the interval Determine the following: (b) Un1Bn 3. Let the universal set be S = {1, 2, 3, 4,...
For each of the following, draw possible diagrams that match the given measurements. Then, calculate the length of side c. If the calculation cannot be made, explain why. a) In ΔABC, a = 13 cm, b = 21 cm, and ∠A = 29° b) In ΔABC, a = 24 m, b = 21 m, and ∠A = 75°.