let A to have0 al an must by

Q: Prove that if alb and alc then a (bx + cy) for all integers x, y.

A:

Q: 2. Let A = 201-18 and /= 2 1 1 2 01 Find A(A+1).

A: A=[2 1      1 2]I=[1 0      0 1]

Q: A. let w-e te Find W2

A: We can solve this using u/v rule

Q: Find the result of the operations indicated in each of the following problems using formulas (F-01)…

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Q: 3. Let A = {1, 2, 3}. What is |A|?

A: If A = {x,y,z}  |A| = sqrt x^2 + y^2 + z^2

Q: |Let A¡ = [i − 1, i] for all integers i = 1,2,3,4. Find the following. a. A₁. A₂- b. A₁ U A₂ U A3 U…

A: The given set Ai=i-1, i for all integers i=1, 2, 3, 4. We have to find, a) A1, A2, A3, A4 b)…

Q: - Let T€ B(H). (a) Show that ker T'T=ker T. (b) Show that TT and TT have the same eigenvalues. (c)…

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Q: Let an = an-1+ an-2 with ao = 0, a1 = 1. Show that an is even iff ( if and only if) n is a multiple…

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Q: Let w be defined as 2 more than the number of digits in the integer w. For example, 15 =4(2 digits…

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Q: ze² = πi) 4 Verify that i is

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Q: Let = [1, -1, 1], [-2, -1, 3] and = [-1, 2, 2]. Find (u ×7)•w: O-14 07 O 10 Does not exist

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Q: Is X and Y are independent

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Q: let A. 2. . find A"

A: We have, A=1201To find An we will calculate A1,A2,A3,... and observe the pattern.

Q: Show that A × B ≠ B × A, when A and B are nonempty, unless A = B

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Q: Determine the orders of the elements of D∞

A: It is known that, D∞=a,b|a2=b2=e also it can be observed that, D∞=abka,abk,bak,bakb Let x∈D∞. If…

Q: 2. Let f and g be permutations. Show that the fgf¯ is the same as the order of g. order of h =

A: our objective is to prove the result

Q: с. In(х + 2) +Inx —D In(x + 12)

A:

Q: Question Solve this system by using 9y = -82 9y-5 4x 7x

A: Let's solve given two linear equations by using Matrix operation.

Q: The linear combination of gcd(252, 198) = 18 is? a. 252*4 – 198*5 b. 252*5 – 198*2 c.  252*5 – 198*4…

A: Given, gcd252,198=18 We, can write the above equation as, 252=1·198+54198=3·54+3654=1·36+1836=2·18+0

Q: . Let A Find A.

A: Given matrix is Firstly, we find A^2

Q: Verify that A → B is equivalent to A ∨ B.

A:

Q: . Let A = 1 03 2 3 4 1 02 Find A-¹ if possible. If A−¹ does not exist, explain why.

A: Given that a matrix A  and we find the inverse of this matix A or A-1.

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

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Q: Consider the vector field F(r. y, 2) = (6yz- 8z) i + (10y + Gu z) j + (6æy – 9c?) k. a) Find a…

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Q: 3A, B E {sets} such that A CBAA= B.

A: To check whether the given statement true or false: ∃A,B∈sets such that A⊆B∧A=B