6.T. Show that if f∈L∞(X,X,µ), then |f(x)|≤∥f∥∞ for almost all x. Moreover, if A <∥f∥∞then there exists a set E∈X with µ(E)>0 such that |f(x)|>A for all x∈E. 6.U. Show that if f∈Lp, 1≤p≤∞, and g∈L∞, then the product fg&#
29 Problems Finite Math. See attached file for full problem description.
Please help with these problems. See attached file for full problem description. 1. Find 2. a) Find the inverse of: . b) Use it to solve the following system of equations: 2x1 + x2 + x3 = 4 x2 + 2x3 = 0 2x1 + 2x2 + x3 = 1.
The three elementary row operations come from a very natural place - they are the matrix equivalent of the same three operations allowed when reducing and solving a system of equations. See attached file for full problem description. Clearly explain, matrix by matrix, how the row operations correspond to operations on t
5. In general, a matrix's row echelon form can vary a bit. A matrix's reduced row echelon form is always unique. In other words, there is only one specific reduced row echelon form matrix associated with each matrix. (a) Consider the following homogeneous system: 2x1 ¡ x2 + x4 + 4x5 = 0 2x1 ¡ 2x2 + x3 + 4x4 ¡ 3x5 = 0 2x
8.1 Exercises Solve each of the following systems by graphing. 10. 2x - y = 4 2x - y = 6 12. x - 2y = 8 3x - 2y = 12 20. 3x - 6y = 9 X - 2y = 3 26. Find values for m and b in the following system so that the solution to the system is (-3, 4). 5x + 7y = b Mx + y = 22 8.2 Exerc
Find the necessary conditions on r1,r2 and n1,n2 that will guarantee a solution to the system: x ≡ r1 mod n1 x ≡ r2 mod n2. keywords: congruent, cogruency
Prove that y^2= x^3+23 has NO integer solutions.
Please see the attached files for the fully formatted problems. 1. Given the equation below, find f(x) where y = f(x). 8y(6x - 7) - 12x(4y + 3) + 265 - 5(3x - y + 2) = 0. 2. Solve these linear equations for x, y, and z. 3x + 5y - 2z = 20; 4x - 10y -z = -25; x + y -z = 5 3. The value of y in Question 2 lies in the ran
Please see the attached file for the fully formatted problems. 1. Write as a decimal. 2. Multiply. (-1)(5) 3. Give the coordinates of the point graphed below. 4. Solve. 8 - (4x - 3) = 19 5. A backyard has dimensions yards by yards. What is the area of the back yard in square yards (yd2)? 6. If a 4.4-pound bag of
There are 3 suspects, A, B, and C, for a robbery that presumably happened in a shop. We know that the following facts are true: (1) Each of A, B, C was in the shop on the day of the robbery, and no one else was there on that day. (2) If A was guilty, then he had exactly one accomplice. (3) If B is innocent, then so is
Row reduce matrix to reduced echelon from. Circle pivot positions in the final matrix and in the original matrix, and list the pivot columns. 1) Find the general solutions of the systems whose augmented matrices are given. 2) 3) Use the echelon form. Suppose each matrix represents the augmented mat
The augmented matrix of a linear system has been reduced by row operations to the form shown. In each case, continue the appropriate operations and describe the solution set of the original system. 1) 2) Solve the system. 3) 4) Determine if the system is consistent. Don not completely solve b
See attached file for full problem description. 1. Graph the inequality. 2x + 3y > 6 2. Given g(x) = -3x + 5, find g(2a) 3. Graph the inequality: x - y < = 2 4. Graph the inequality: y > =3x 5. Given f(x) = -x^3 - 3x^2 -3x +9, find f(-2), f(0), and f(3) 6. Given f(x) = -5x - 1, find f(-2) 7. Graph f(x) = 4x + 1 8. Grap
1. A coffee merchant has coffee beans that sell for $9 per pound and $12 per pound. The two types are to be mixed to create 100 lb of a mixture that will sell for $11.25 per pound. How much of each type of bean should be used in the mixture? 2. In a town election, the winning candidate had 220 more votes than the lose
Find values for M and B in the following system so that the solution is (-3,4) 5X + 7Y=B MX + Y=22
Prove the real numbers, R, contain a subring A with 1 Є A and A maximal (under inclusion) with respect to the property that 1/2 not Є A [Use Zorn's theorem]. See attached file for full problem description.
#14 Solve each system by the substitution method. Indicate whether each system is independent, inconsistent, or dependent. #24 Graph and solve the absolute value equality. #46 Graph each compound or absolute value inequality. |x-3y| ≥ 9 Please see the attached file for the fully formatted problems.
Solve each system by the substitution method. Section 7.1 #54 X + 3y = 2 -x + y = 1 Section 7.2 #64 Book and magazines. At Gwen's garage sale, all books were one price, and all magazines another price. Harriet bought 4 books and three magazines for $1.45 and June bought two books and five magazines for $1.25. What was th
The solution of following system of linear equation is: 2x-2y+3z=1 5x-6y+10z=2 2x-4y+9z=1 x=2, y=3, z=1 And the solution of this system is: 2x-2y+3z=1 5x-6y+10.1z=2 2x-4y+9z=1 x=2.375 y= 3.75, z= 1.25 (You do not have to show this) Comparing the 2 solution can you determine whether the fist system of equat
1. Sam needs to get carpet for two rooms of his house. Estimate the number of square feet (square footage) in the two rooms if one room measures 10 ½ feet by 9 ¾ feet; and the other room measures 19¼ feet by 18 ½ feet. 2. Sandra drove for 234.8 miles and used 12.6 gallons of gas. Estimate the number of miles Sandra's
Prove that there exist at most 2 non-isomorphic fields of order 4.
Analyze the stability of the fixed points of linear differential systems. Provide several explicit examples, with graphical illustrations
1. Consider the system of equations x + y + 2z = a x + z = b 2x + y + 3z = c Show that for this system to be consistent, the constants a, b, and c must satisfy c = a + b. 2. Show that the elementary row operations do not affect the solution set of a linear system. 3. Consider the system of equations ax + by =
Solve each equation and check your answer 2(a-4)+4=5(9-a) Solve each equation. Identify each equation as a conditional equation, an inconsistent equation or an identity. Solve each equation for y. Write the equation in the form of y=mx+b where m and b are real numbers Find the value of y in each formula if x=
Please explain how to prove the identity with the following example: sin x - sin 3x / cos x - cos 3x = -cot 2x
Prove that is p is prime, we have: n choose m is congruent to [floor(n/p) choose floor(m/p)]*[(n mod p) choose (m mod p)] (mod p) Hint: show that (1+x)^(pq+r) is congruent to (1+x)^r * (1+x^p)^q (mod p) If you can point me to a book or website explaining how to do this type of problem, and give a sketch of the proof,
Show that all automorphisms of a group G form a group under function composition. Then show that the inner automorphisms of G, defined by f : G--->G so that f(x) = (a^(-1))(x)(a), form a normal subgroup of the group of all automorphisms. For the first part, I can see that we need to show that f(g(x)) = g(f(x)) for x in
1) Solve by the addition method. 3x + 2y = 14 3x - 2y = 10 2) Solve by the addition method 5x = 6y + 50 2y = 8 - 3x 3) Solve. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. 4) Can't type fractions, so