Show if gcd(a, b) = 1 and a\x and b\x Then a b\x

Q: a a +1 2² (² + ¹ + x² = 1 [(¹-x)² + (1 + x)² ] F1 2 2 2

A:

Q: Let u = (3, 5, -7) and v = (6, -5, 1). Evaluate u + v and 3u - v.

A:

Q: Let a=⟨3,−5,5⟩ and b=⟨−1,5,2⟩ Find the component of b onto a

A:

Q: Show that both ℝ and ℝ2 may be covered by countably many open balls.

A: The answer provided below has been developed in a clear step by step manner.

Q: J1, 1), К(3, 2), L(4, 1) and M(6, 1), N(5, 2), P(2, 1) 3)

A: Below Image has the graph with points plotted on Coordinate Axes.

Q: 14 of 14 egbu A normal curve with a mean of 70 and a standard deviation of 20 is shown. Shade the…

A:

Q: Z

A:

Q: Show that (A\B)\CC A\C.

A:

Q: Let A = (1,2), B = (1,3,4) C (2,3, 4} and U = (1,2,3,4,5), then [Cn (B- A)] = O {3.4} O {1.2} O {3}…

A:

Q: Show that <a, b | a5 = b2 = e, ba = a2b> is isomorphic to Z2.

A: To show that the group <a, b | a^5 = b^2 = e, ba = a^2b> is isomorphic to Z2, we need to…

Q: Show that is isomorphic to Z2.

A:

Q: 2. (6 marks) Let a, b, c € Z with a 0. Prove that if a X (a + 2b + 3c), then a Xb or a Xc.

A:

Q: EXER 7: MATRICES Prove that if N is invertible then MN¹ = N¹M if and only if MN=NM.

A:

Q: Express the following as linear combinations of 1= (2, 1, 4), v= (1, – 1, 3), and w= (3, 2, 5). 8.…

A:

Q: X and  Y are randam variables then XeY is a randam variables.

A: Here, The X and Y are two random variables  Then XeY are also random variables we have to show Here…

Q: Justify is it true or false? It is possible for variables to have r=0 but still have a strong…

A: If the relationship is linear between variables, then r = 0 means that there is no correlation…

Q: If then A-¹- = A = [1 0 0 07 3 1 0 0 24 1 0 8 55 1

A: The given matrix, A=1000310024108551 We have to find an inverse matrix of A.

Q: If a = (2, 0, 2), b =(4, 2,-2), and c = ax (bx c) = (a x b) x c = = (0, 2, 5), show that a x (bx c)…

A: The answer is in step2.

Q: Compute u – 3v, u v and u x w.

A:

Q: Show that if a \ b and gcd(b, c) =1 Then gcd(a,c) = 1

A:

Q: Let A=(1,2,3,4), B=(00,01,10,11), C3(x,y,z). f1 = (1,00),(2,01),(3,01),(3,10) (4,11)} f2 = {(1,x),…

A:

Q: Show that <a, b | a5 = b2 = e, ba = a2b> is isomorphic to Z2.

A: We have to show that <a, b | a5 = b2 = e, ba = a2b> is isomorphic to Z2.

Q: 1. Solve the equations below. Show your work. a.) x2 – 14x + 45 = 0 b.) 3x2 – 2x - 5 = 0

A: As per our company guidelines we are supposed to answer only one question kindly post other question…

Q: Let S={(0,-1,1),(0,-2,-1),(1,1,2)}.

A: S?

Q: Let A {a, b} and B = {1, 2}. Give an element of A x B x A.

A: Let M and N be two sets. The Cartesian product, M×N is the set of all possible ordered pairs with…

Q: Let A = {h,1,o}, B = {7,8), C = {7}. AXBXC = { CXBXA = { BXBXB={

A:

Q: Compute A B, where A AB= 0 -2 2 -2 0 2 -4 7 8 -5 -1 2 and B = 8 -2 1 -5 -1 3

A: This question can be solved using the concept of multiplication of matrices.

Q: Let Ai = = [i, i + 1], i = 1, 2, 3, Then A₁ A2 A3 A4 is. a. {1,2,3,4,5} b. (1,5) d. [1,5] ....

A: We have given that Ai=[i,i+1]A1=[1,2]A2=[2,3]A3=[3,4]A4=[4,5]

Q: If u x = [1, -3,5], thenx =

A: