Show that quaternion multiplication is not commutative. (That is, give an example to show that sometimes {n+ ng. ) ((Actually, a few examples are printed on the previous page.))

Q: The representation of an even integer is 2k; and that for odd is 2k+1 or 2k-1 for some integer k.…

A: To show the representation of an even integers is 2k and that for odd integer is 2k+1 or 2k-1 by…

Q: The answer is incorrect because the question requires to prove it without fully expand the terms.…

A: This question can be solved using the concept of general term of binomial expansion.

Q: In the expression (x+y)', the exponent represents repeated multiplication, so the expression may be…

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Q: 1. Prove that multiplication of complex numbers is associative.

A: We know that a complex number in the form of a+ib  i.e. z= x+iy =(x,y) where x and y are real…

Q: Suppose that {an} is defined recursively by: an = (an-1)² - 1 and that ao = 2. Find a2 and az.

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Q: Problem 4 [25 points]: Contradiction Given a proof by contradiction of the statement: If n? + 11 is…

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Q: Prove that N × N × N is countable. Does your argument generalize to the Cartesian product of k…

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Q: Show by contraposition that : Vx ERx?-7x-820 - x2 8 or x S-1

A: In this method, we prove negation of antecedent and get contradicted and get our required results.

Q: Question 17 What is the expanded form of (3x +4)*? 8 Lx+256 B. 81x + 432x + 864x+768x + 256 .2 C.…

A: Option B is correct.

Q: Can you explain what happens with the I's (identity) on the multiplication? I dont really understand…

A: We have explain the property of identity matrix.

Q: The nth row of Pascal's triangle lists the coefficients of (x +y)^.

A: Here draw pascal triangle for some 1 to 4 rows and conclude for nth row

Q: A bit string contains 1's and O's. How many different bit strings can be constructed given the…

A: There are a total of 10 positions in the first half of the string. To accommodate exactly 7 1's, we…

Q: (15) Let a, b = Z. Prove that if a is divisible by 4 and b is divisible by 4, then: (a) ab is…

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Q: Compute ||w| using w= ||w|| || = 7 5 -4 (Type an exact answer, using radicals as needed.) LO

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Q: Write the fourth term of the expansion of (2x+ 3y)°.

A: We can get desired result by two ways. One is by opening binomial expansion then getting fourth…

Q: ply DeMorgan's Laws un - && (Ir || a))

A: Introduction: The formula for de morgan's law is given by, ~(a∧b)=~a∨~b~(a∨b)=~a∧~b

Q: Determine the multiplicative inverse of 11 in Z24. Your final answer should be an element of {0, 1,…

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Q: Multiply 4/3 ∗ 9/12 using any method/representation and explain your reasoning.

A: The given expression is 43×912. Rewrite the expression 43×912: 43×912=43×3334

Q: Give a conjecture about algebra and solve it

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Q: Question# (1) You're trying to compute [–dx and deg(f)2deg(g), what should you do first? a) Try…

A: Please see the explanation below

Q: Suppose that an is defined recursively by an an-1-1 and that a = 2. Find a3. = ao = 2 a₁ = =a² - 1 =…

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Q: Find the conjugate of the expression. √7-z

A: We know that if z=x+iy,x,y∈ℝ then conjugate of z is z¯=x-iy .

Q: Please help quick thanks

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Q: Show that [-a, b] is the additive inverse of [a, b] in Q.

A: To Prove -a,b is the additive inverse of a,b in ℚ. By definition of additive inverse, For y in ℝ,…

Q: O Question 10 of 12 b=0b 0 (4 3i)(4+31) D 0 (4-3i)(1) (61)(4+31) (61) (1) D (-5)(4+3) D B (-5)(4)…

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Q: (a) Find an integer n > 2 such that all nonzero elements of Zn have multi- plicative inverses. (b)…

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Q: 10. Determine the product of i2n-1 &. i2n+1 Use exponent properties to simplify and then, based on…

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Q: Use Pascal's Triangle to expand (5 + 2y)*.

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Q: Let M = Find formulas for the entries of M", where n is a positive integer. Hint: a formula such as…

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Q: What is Googol?

A: Googol is a number 10100.

Q: First find gcd(213, 11), then find the inverse of 11 mode 213.

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Q: Find the value of (1+ i)148 – (1 – i)'48 Do not just state the answer. Show your computations.

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Q: Use your work from problem 2 and the method used in the example at the end of Lecture 16 to solve…

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Q: Show that the system consisting of all elements of the form a+b√5, where a and b are any rational…

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