Use the given LU factorization to find all solutions to Ax = b 0 5 1 0 0 15 A = 4 1 0 0 -2 |, b 54 -6 4 1 -114 X =

Q: Find the two smallest positive solutions of 5sin(5x)=3

A: 5sin(5x)=3 sin(5x)=.6 sin(5x)=sin36.87°

Q: For which values of a and m does ax = 1 have a solution in Zm?

A: Claim:

Q: 5 + 6 x 2- 22 25. 7 3 3 - X 3 3 x 6

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Q: Verify that (AB)T = BTAT.

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Q: Solve the given SLE using LU-Factorization X, +x, +x3 = 3 X, - x, + 4x; = 4 2x, +3x, – 5x; = 0 -

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Q: The set of solutions to z =-V2 - V26 is

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Q: For which values of a, b, and m does x + a = b have a solution in Zm?

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Q: Prove that there exists at least one solution to the equation 4x+ 3x +1 = 4x2.

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Q: Show that ri =1+i, r2 = 1-i is a solution of (3+ i)x + (1+ i)x2 = 4 +4i %3D

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Q: Select all equations that are equivalent to x2 + 6x = 16. O x² + 6x + 9 = 0 O x2 + 6x + 9 = 16 O x2…

A: Use the formula x2+2xy+y2 = (x+y) 2

Q: 3. Show that (1+i) = 2i

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Q: Find the value of ‘v’ in v2 – 2v -15 = 0, if v is a natural number.

A: Given quadratic equation is,

Q: Suppose an = 4an – 1 + 6an – 2 a4 = 96, a5 = 430, and a6 = 2276. Find а1, а2, and аҙ. аз. a1 Preview…

A: Here, recurrence formula is, an=4an-1+6an-2-2an-3

Q: 2. Solve the given SLE using LU-Factorization X- X, +4x, = 4 2x, +3x,-5x, = 0 .

A: x1+x2+x3=3x1-x2+4x3=42x1+3x2-5x3=01111-1423-5x1x2x3=340Now, A=1111-1423-5, x=x1x2x3,  B=340

Q: The product of 2x³ + 3x² +1 and 2x²+ 4 in z5 [x]/ is: O 5x^2+ 5x +1 4x+1 О х^2+2 None

A: Given factor ring is ℤ5xx3+1 where ℤ5x is a polynomial ring over ℤ5. We have to find the product of…

Q: Solve the following IBVP: 0 0, u(x,0) = 2 – 2x2, u(x,0) = 0, 0 0, %3D %3!

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Q: B. Verify if the given values of x are solutions to the equations/ ined 1. 7x + 2 = 9 2. 3x-5 4 srps…

A: 1. 7x+2=92. 3x-5=43. x+8<64. -4x≥15. 3x+1≥7

Q: 1. Given that r + px+q and 4x +q have a factor (x-r) where p,q and r are non-zero. Show that 4p…

A: topic - quadratic equations

Q: Solve for u. u+5=5 ?

A: Multiply with 5 on both sides

Q: For which values of a does ax = 1 have a solution in Z5?

A:

Q: By using the iterative formula Xn+1 and xo = O O 0.3652 O 1.3652 O2.6352 = 1.5, then the value of x5…

A: Find the value

Q: Find all integer solutions of 3x + 5y + 12z = 20

A: Solve

Q: Prove BCスツ+)B[スかリック =B(X1y)

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Q: Perform the indicated calculations. 2(2 + 1 + 2) in Z3

A: Given that, Perform the indicated calculations. 2(2 + 1 + 2) in Z3 It means, firstly we have to…

Q: Calculate the value of 1n(-V5 – V5i )

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Q: 6. Show that (1) Cou(B1, g) = 0 (2) Cov(3o, B1) %3D

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Q: Select all the equations that are equivalent to 8k= 20. %3D 8k - 4 20 +4 O 8k X 3= 20 X 3 O 8k X 5=…

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Q: Find the general solution of у "— 2у "— 16у'+ 32у -0 given that r = 2 is a root of the…

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Q: Solve the followig 13. BauSsian or Eduss Jordan Using E lemination. 5x, +6x=7X 3D0 3. ース×,+ 3X7…

A: Answer

Q: Use the given LU factorization to find all solutions to Ax = b. [1 0][9 A = 5 1 -2 112 b = 546 181 x…

A: Value of x=(X1,X2)=(-7,-7) See below

Q: Consider a LU factorization of -2 1 3 A = 1 4 -2 -5 as A=LU. Then L2,1 and U1,1 are respectively…

A:

Q: The Cholesky factorization of 53 is UTU where U is: 3 2 V5 5 -3 V5 1 3. 0 1/5] V5 5 3 0. 1

A: The given matrix is,5332

Q: show that x'-15x +C= O has at most root on E2,2] one

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Q: Eliminate the arbitrary constant in x^3 - 3yx^2 = c. *

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Q: The product of 2x3 + 3x? +1 and 2x2 + 4 in zs (x]/ is: O None O 5x^2+ 5x +1 O 4x+1 x^2+2

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Q: Show that the equation In(x + 1) = In(x²) has at least two real solutions.

A: we need to show that ln(x+1)=ln(x2) has at least  two real solutions.

Q: Use the Cayley - Hamilton theorem to calculate 3 -2 -1 A-1 and A4 if A = 3 4 -2

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Q: 3. Find the general solution to: xi = 4x1 + 2x2 + 3et x2' = 2x1 + x2 + et. %3D

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Q: Find Re(z) if z(2 + i) = z+(16 + 20i)

A: Given that, z2+i=z¯+16+20i. The objective is to find Rez.       For any complex number z=a+ib, its…

Q: В Calculate A and B so that + %D 1+x 1-

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Q: Solve the given SLE using LU-Factorization X, + x, +x3 = 3 X, - x, + 4x3 = 4 2x, +3x, – 5x, = 0 -

A:

Q: Use the LU factorization to find all solutions to Ax = b. [1 0 01 [4 - 2 1 0 0 8. - 6 1 A = 0. 1 0…

A: Value of x=(X1,X2,X3)=(3,-2,0) See below the calculation

Q: Prove that there are no solutions in integers x and y to the equation 2x2 + 5y² = 14.

A: Two different proofs are given for the given problem as follows :

Q: Find Re(z) if z (2+i) = z + (16+20i)

A:

Q: Use the given LU factorization to find all solutions to Ax = b -7 4 9 |,b : 1 0 01 -7 1 0 -1 7 1 -39…

A:

Q: Find the number of integer solutions of X +x, +x, = 10 subject to the conditions given. a. 저20,%…

A: Integer solution

Q: The set of solutions to z^6=−i is?

A: We have to find The set of solutions to z^6=−i.

Q: In ARST, mZR = (6x + 10)°, mZS = (2x + 5)°, and mZT = (3x – 11)°. Find mZR. -

A: The sum of three angles of a triangle is equal to 180°. Equate the sum of the given three angles to…