Prove that Let T be a linear operator on V, and suppose that the minimal polynomial for T is irreducible over the scalar field F. Then T is semi-simple.

Q: Let phi / Q * (sqrt(2)) -> phi(sqrt(2)) be the map given t phi(a+b sqrt 2 )=a-b sqrt 2 . Show that…

A:

Q: 35) y+ y, =-5cos(2t), y+y, = 5cos(2t), y;(0) = y{(0) =1, y,(0) =-1, y,(0) = 1.

A: The solution is given as

Q: Consi der the lines : = 2 - y = z+1 and l2 : = y - 2 = 1. Determine a direction vectors for the…

A:

Q: Determine whether the graph represents y as a function of x. Explain your answer. (a) y 12 (9, 10)…

A:

Q: The chemical epinephrine (more commonly known as adrenaline) has the chemical formula CH(OH),C3H,NH.…

A:

Q: Is the vector [1 0 0]' a linear combination of the columns of 5 -2 ? Why? B = 3 -1 5. 3 2 129

A:

Q: Find the solution of the equation = e cos y dy? which tends to zero as x → 0o and has the value cos…

A:

Q: 1 B = -2 -2 ? Why? -1 5. 327 3. :-

A:

Q: A plant produces newsprint and rolls of paper are fnspected for defects, The number of defects…

A:

Q: d – 2g f – 2i 3c -а + 4g -b+ 4h -с+ 4il е — 2h 3b a b с Let |4| = |d e f = 2 and B = За g hi

A:

Q: Prove that 17 is the only prime number of the form n²- 64.

A:

Q: What is the square root of -5?

A:

Q: Determine if the sequence {an} converges or diverges. Find the limit L if the sequence converge. an…

A:

Q: Q6: Solve for matrix X in the matrix equation X- A" = 21, where I is a unit matrix with size 2 x 2…

A:

Q: Ql: Given that A = [3 -3 -5] and B = | 5,what is the matrix A - BT? 352

A:

Q: Prove that l17 is the only prime number of the form n²- 64.

A:

Q: 4. (i) Consider the 3 x 3 permutation matrix 0 1 0 P = |0 0 0 1 1 0 0 Find all 3 x 3 matrices A such…

A:

Q: 1) Find all integral solutions of the linear Diophantine equations бх + 11у %3D 41

A: Here we use the euclidean algorithm to solve the Diophantine equation

Q: 3. Consider the vector space V p<? = {ax? + bx + c : a,b, c E R} of quadratic polynomials. Let B be…

A:

Q: use triple integral to find the volume inside x2+y2=4x, above z =0, and below x2+y2=4z

A:

Q: 5. (i) Let 7 be a permutation on {1,2,.,n}. The matrix Pr for which pi. = e-(i)• is called the…

A:

Q: Let D-{tx.y.2) : 2+y?s2s 1, z2 o}. Evaluate z dv.

A:

Q: Transform to normal form and solve (showing the details!) 37. иху

A:

Q: Let f be a function admitting continuous second partial derivatives such that Vf(x, y) = (ax? + a?x,…

A:

Q: You deposit $6000 in an account earning 7% interest compounded monthly. How much will you have in…

A:

Q: nis question we prove that certain sets are not convex. each of the following sets, give the…

A:

Q: * For the following data (2,2,4,6,8,10,12) 7 12 4 6.29 10 6. Мean equal Median equal Mode equal…

A:

Q: Let V be the space spanned byf1 = sin x and f 2 = cos x. (a) Show that gi = 2sin x + cos x and g2 =…

A: We know that Span is a set, the linear combination of elements of which form the whole space

Q: Consider the lines : = 2 - y = z + 1 and l2: = y - 1. Determine a direction vectors for the lines (1…

A:

Q: If you are asked to apply Euler's method with (xo, yo) = (1, 7) and step size h = 0.5, how many…

A: As here given the initial condition (x0,y0)=(1,7) and h=0.5. And here we calculate for x=3 .…

Q: Solve the system using either of the three direct methods 1. a- 2y + 2z = 3 2x – 3y – z = -7 -* + 3y…

A: Given systems are solved using Gaussian Elimination Method.

Q: Find the series' radius of convergence. sn=∞ (-1)"(z+2)" m=1 (n+1)! O o, for all x O 0, for all x…

A: Radius of convergence

Q: Prove that l17 is the only prime number of the form n²- 64.

A: We have to prove that 17 is only prime number of the form n2−64. Since, n2−64=n+8n−8 Let for some…

Q: Summing Series (numeric summation): Tylor Series: x2 x3 x4 M -1- x+ e-X = 2! 3! ..... 4! 5! n=0…

A: We have to find the exact exponent and sum of series upto that terms.

Q: 2. A particle is moving along a line with velocity given by the function v(t) =t tanh(ln t)[sech(ln…

A:

Q: B. Use the facts in the table to solve each problem. Element Melting Point 1064.43°C 327.5°C Gold…

A:

Q: use the Euclid's algorthim to find the inverse for 76 mod 83

A:

Q: Find the general solution for the following differential equations: (a) (1 – xy + x²y²) dx + (xy³ –…

A: As per policy, we are allowed to answer only one question at a time. So, I am answering the second…

Q: What is the principle part for f (z)

A:

Q: 12. Consider the solid Q bounded by the surface of equation z = x*+ y° and the plans z = 4, yv3 = x,…

A:

Q: Find all max/min points of the function sin x f(x) = COS X on the interval [0,10] by using the…

A: To find all the maximum and minimum points of the below function on the interval [0,10].…

Q: Use a definite integral to find the area bounded by the curve x+3, the axes over the interval…

A:

Q: . Find the parametric equations of normal line to the surface given by f(x, y) = tan vx² + y² at the…

A: Given,           f(x, y)=tanx2+y2,  at π2, π2, 1

Q: a) Given the vectors in R3 v, =(11 -3), vz= (1 -3 1), v3=(-3 11) Using the system of linear…

A:

Q: 161 n + e 20 n ( 2n + tan (103 n). 00 The sequence is n=1 O divergent as its limit is o0 161 O…

A: The given sequence is ln161n+e−20n2n+tan−1103nn=1∞. Here, an=ln161n+e−20n2n+tan−1103n Now,…

Q: Find an equation of the curve having all these properties. • It is a solution to = 12r² – 10. • The…

A:

Q: 2. At what point on the line y = b does the line segment from (0,0) to ( a,0) subtend the greatest…

A: at what point on the line y=b does the line segment from 0,0 to a,0 subtend the greatest angle.

Q: How would you create a parallel line that passes through a given point using rotation?

A:

Q: Can you explain number 2? How did you know that is the formula to use?

A: Let V be a vector space over R  Define a function ·:V x V→ℝ Then the function is said to be inner…

Q: Show that for every positive integer n there exists an irreducible polynomial of degree n over Fp.

A: