5. In the ring (Mat,x2(Z), +,.), if A € Matzx2(Z) then the ideal (A) = (a) {B. A: BE Matzx2(Z)} (b) {B. A + n. A: BE Matzx2 (Z) and n e Z} (c) Matzx2(Z) (d) No Choice (a) (b) (c) O (d) 6. In the ring (Z99, +90,-90 ), the ideal (10) n (15) = (a) (80) (b) (75) (c) (60) (d) No Choice

Q: 1. The remainder of p(x) = x² + ax³ + bx² + 5x by x² + 3x + 2 is -3. Find a, b 1 divided

A:

Q: Prove that ithe polynomial PCO =-2xP +2x2+loxx t6 has and fachor azero at M= 3, and fachm s ala the…

A: The given polynomial is px=-2x3+2x2+10x+6. It is given that x=3 is a root of the polynomial. If x=3…

Q: Use the inner product = aobo+ aıb1+ azbz+ asb; to find , lIlp|], d(p, q), and then find the angle…

A:

Q: 2. Let Z [√2] = { a+b√2 la,be Z}. Define addition and multiplication on Z[√2] as follows: (a+b√2)+(c…

A:

Q: 3-41 2-2₁ 3-2₂ B(z₂), C(3), and D(2) (taken in clockwise sense) are concyclic. If 2-22 2) = k (k>…

A:

Q: 2. Show that (p→r) v (g→r) and (p ^ q) → rare logically equivalent.

A:

Q: Use the inner product (p, q) = abo + a,b, + a,b, to find (p, q), ||p ||, ||9||, and d(p, q) for the…

A:

Q: One of the following is an ideal of z1: (0,3} (0,2,4,6} None (9,3,6,9}

A: From given statement

Q: 2) Let R real numbers, define = x,Y1 +4x2y2 + 6x3Y3 for x = (x1,x2, X3) and y (y1,y2, Ya). Is inner…

A: Let V be a vector space over ℝ.An inner product <·,·> is a function V×V→ℝ with the following…

Q: 6. (10pts) Determine whether you can find the interpolating polynomial p(t) = a, + a,t + a,r² for…

A:

Q: 7. Find a pair of integers (x,y) such that 4021x + 2014y= 1.

A:

Q: 2. Factor. a) x² 18x + 81 b) x² - 2x - 15 c) x² + 2x - 24 d) x² + 6x-40 e) x²+x-30 f) x² + 3x-35 g)…

A: Please follow the next step.

Q: 13. Let P(x) be the degree 10 polynomial through the 11 points (-5,5), (-4,5), (-3,5), (-2,5),…

A: We will find the value of P(6) using the Newton's forward difference interpolation polynomial of…

Q: (a) If a, b,c € Z+ and a +b=c then (c,[a, b)) = (a, b).

A: As you asked multiple questions , so I solved only the first one.

Q: If x,y,z are real numbers satisfying the equation 25 (9x* +y° )+9z²-15(5xy+yz+ 3zx )=0 then prove…

A:

Q: For what values of a does the homomorphism system (b – 1)x + 2y = 0 2x + (b – 1)y = 0 Have a…

A:

Q: 4. Show that if x, y, z are integers such that x2 + y2 + z? = 2xyz, then x = y = z = 0. (H)

A:

Q: Use the inner product (p, q) = abo + a,b, + a,b, to find (p, q), ||p ||, ||9||, and d(p, q) for the…

A: Since you have posted a question with multiple subparts, we will solve the first three subparts for…

Q: Use the inner product (o, 9) = 2obo +a1b1 +a2b2 to find o, 9), |P||- |||, and d(p, a) for the…

A:

Q: In Exercises 10-11, add the polynomials. 10. (-8r³ + 5x² – 7x + 4) + (9x³ – 11x² + 6x – 13) 11.…

A: since you have asked multiple questions in single request so we will be answering only first…

Q: 7. Show that (a). (Z, +) # (Q, +). (b). (Q,+)# (Q\{0},.). (c). (R\{0},-) # (Q\{0},.). (d). (R\{0},-)…

A:

Q: 11| Q1) If A--2 -1,B 3 3 4 -5 -1 -1 13 -1 Find (–1 x A) + (B + C)

A: