MATEMATIK MATHEMATICS 5 Polinomlar Polynomials 1. P(x)-(a-b-4)/x+(a+b-12)x1+6x+4 5. 2 Yant/ Answe...
Q6 (4+3+3+ 6=16 marks) Let Xo, X1, X2 be three distinct real numbers. For polynomials p(x) and q(x), define < p(x),q(x) >= p(xo)q(x0) + p(x1)q(x1) + p(x2)q(22). Let p(n) denote the vector space of all polynomials with degree more no than n. (i) Show that < .. > is an inner product in P(2). (ii) Is < ... > an inner product in P(3)? Explain why. (iii) Is <,:> an inner product in P(1)? Explain why. (iv) Consider Xo =...
C1=5, C2=2
C1 a. How many monic polynomials of degree two are there in Zc[x]? b. How many polynomials of degree two are there in Zc-[x]? c. Is x2 + 4x + 5 is reducible over GF(p), where p is the largest prime <C?
[11] Simplify the algebraic expression. (3x² + 2)(7)(x - 4) – (x – 4)?(32(3x’ + 2)?(6x). ((3x + 2))? [12] Find f(x + h) – f(x) with f(x) = -3x + 4x.
Question 4: 4. Show that the following polynomials form a basis for P3 1 - x, 1-x2 1 +x _X 5. Show that the following matrices form a basis for M22 -8 1 0 3 12 -6 -4 2 _ 13. Find the coordinate vector of v relative to the basis S = {v1, V2, V3} for R3 (a) v (2, -1 3); vi = (1,0, 0), v2 = (2, 2, 0) Vз — (3, 3, 3) (b) v (5,...
Please help with each box of the problem.
EXAMPLE 5 Evaluate 7x2 - 6x + 16 x3 + 4x dx. Since x3 + 4x = x(x2 + 4) can't be factored further, we SOLUTION write А. Bx + C 7x² - 6x + 16 x(x2 + 4) + Multiplying by x(x2 + 4), we have 7x2 - 6x + 16 = A(x2 + 4) + + Cx + 4A. Equating coefficients, we obtain A + B = 7 C =...
2 points) Let H be the subspace of P2 spanned by 2x2 - 6x +3, x2 -2x 1 and -2r221 (a) A basis for H is Enter a polynomial or a list of polynomials separated by commas, in terms of lower-case x . For example x+1,x-2 (b) The dimension of H is c)Is (2x2 6x +3, x2 - 2x +1, -2x2 +2x 1 a basis for P2?
2 points) Let H be the subspace of P2 spanned by 2x2 -...
(4 points) For the tableau, P. 0 0 1 X1 5 2 -12 X2 1 1 -5 S1 1 0 0 S2 RHS 0 30 1 47 0 0 perform one pivot operation and enter the resulting matrix below. The pivot element has a box around it. X2 X1 S1 RHS ON
8. Using Chain Power Rule a) ∫ (3X^2 + 4)^5(6X) dx b) ∫](2X+3)^1/2] 2dx c) ∫X^3](5X^4+11)^9 dx d ∫(5X^2(X^3-4)^1/2 dx e) ∫(2X^2-4X)^2(X-1) dx f) ∫(X^2-1)/(X^3-3X)^3 dx g) ∫(X^3+9)^3(3X^2) dx h) ∫[X^2-4X]/[X^3-6X^2+2]^1/2 dx
12. Let m(x)=x2 + 4x + 1 in F5 [x]. Find polynomials f(x),8(x) in Fs [x] so that (x – 3)f(x) = (x – 3)(x) (mod m(x)) but f(x) # 8(x) (mod m(x)).
Please send the detail solution ASAP
Assume X = [X1, X2, X3, X4]T ~ N(µ, C). Consider [1 2 2 6 7 8. µ = E[X] C= 3 7 11 12 4 8 12 16 o What is the pdf of px,(x) ? o What is the pdf of px1,X3(x1, 13) ? O Determine E[X2] ? O Determine E[X2 + X3] ? O Determine E[(X2 – X2)²] ? O Determine E[(X2 – X2)(X3 – X3)] ? O Determine E[X2X3] ?