5. (a) If r23 = 0, prove that R₁ (23) = (23) = 712 + 7³1 01-23 = (1 - 12 - 13). 07.

Q: . What is the coefficient of a" in (2 – x)"?

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Q: ) and () -1 -2 -1 4/ 2 0 The product of

A: The given matrices are: A=-1322      and     B=-20-14

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A: We have to find the remainder when x51 is divided by x+4 in Z7x. Let t be the remainder when x51 is…

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A: Deriving the explicit formulas:The recursive relationship for honey bees is: he+1 = 2he - 4, 87+1 =…

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Q: We have considered the case of regular deposits at the end of each month. If deposits are made at…

A: Deposit at the end of each month: Time period:  yearAPR: Balance after  deposits

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Q: in (4) d. [5in(x+6) - In(x) - In(x² - 25)]

A: Solve the expression

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A: we need to solve (2x-5)+(3x2+7x+10), This is a simple problem based on addition of polynomials.…

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A: Given

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A:

Q: If the sum of the coefficients of all even powers of x in the product (1 + x + x² + ... + x2n) (1 –…

A: Introduction :

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A: This is an arithmetic series with common difference (3-1)=2 And this has n terms in it So we use the…

Q: 14. (−1+i)¹⁰ = ? (Convert to a + bi form)

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Q: 1. (a) 2 Let = (1, 0, -2) and = (-4, 2, 3). Find a real number x such that (ট' –æè) ⊥ à. (b)-1 (c) 3…

A: Let .To find a real number  such that .

Q: MPLETION. Fill-out the missing information on the table, perform the necessary operations. Show your…

A: Note- Since you have posted a question with multiple sub-parts, we will solve first three sub-parts…

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A:

Q: 2 4. Express 989 = 23 43 in the form x² + xy + 5y².

A: The given number is 989. The objective is to express the given number in the form of x2+xy+5y2.

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A: Answer and explanation is given below...

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Q: Q9. (a) (i) Calculate (2 + i√5)(√5 - i). (ii) Hence verify that (√5 - i) is a root of the equ

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Q: -(-6) ± V(-6)² – 4(3)(-3/4) +t = 3t2-6t - 2(3) 6 ± V36 + 9 =t = 6土V45 + t = 6+ 3/5 2士V5 +t = 2 +t =…

A: Explained below

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Q: Describe geometrically the effect of the transformation T Let A = -(1) Define a transformation T by…

A: We are authorized to answer one question at a time since you have not mentioned which question you…

Q: 2. Let k be a complex number and P(x) = 8x³ − 4kx² + (2k+6)x +3. Find all values of k for which P(x)…

A: Given the polynomial  P(x)=8x3−4kx2+(2k+6)x+3 , we need to determine the value(s) of  k  such that…

Q: (a) Explicitly check that [7] + [21] = [98] + [–5] in Z13- (b) Find another value of n such that [7]…

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Q: a) Show that x = 1+2i is a root of p(x) where i = surds(-1). b) By using the fact that p(x) is a…

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Q: 2. (a) Show that (z − 1)(26 + 25 + 24 + z³ + z²+z+1) = z7 - 1. (b) Show that if ¢ is a 7th root if…

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Q: Factor 10+ 4i into product of primes Z [i], (Hint: Ille= (2)(2)(29)) in %3D

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Q: In(5x + 2) In 3x Solve lim

A: We can find the limit as below.

Q: (2x-3y) =

A: