If T:R² R³ is a linear transformation and the action of I on the special vectors U and V is as given, find a formula for T(X), where X is any vector in R2. -9 U = = V = 7 T(U) = 14 -15 T(V) = -18 19

Q: Find the half range Fourier cosine series expansion of the periodic function, f(x)=x-x, 0≤x≤n.

A:

Q: If To, T₁, T2, ..., T, represent the terms in the expansion of (x + a)", then find the value of…

A: From Binomial theorem we have              x+an = C0n xn + C1n xn-1a +  C2n xn-2a2 +  C3n…

Q: If one quarter of all 3-subsets of the integers 1, 2, ..., m contain the integer 5, determine m

A: This is a problem of counting.

Q: Draw a graph that is Eulerian but not Hamiltonian.

A: To draw a graph which is Eulerian but not Hamiltonian.

Q: B. Find the volume of the indicated solid i) under z = x² - y² and above the square R = [1,3] ×…

A:

Q: 2. (5) Find f, for the function f(x, y) = sin (x + y²)

A:

Q: a) Solve X4+12X3−13=0, correct to 4 significant figures by an algebraic method of successive…

A: (a) We can use the bisection method to find the solution to the equation.  We have f(X) = X4+12X3-13

Q: Write the base two numeral 110000, in expanded form. (1x2)+(1×25)+(0×2¹)+(0×2³)+(0×2²)+(0×2¹)=96…

A: (110000)2 =

Q: 9. Show that if a is a root of X²-bX+c with b, c integers and 6² - 4c < 0, then there are only…

A: Given that α is a root of X2-bx+c, with b,c integers and b2-4c&lt;0. Since b2-4c&lt;0, therefore…

Q: Let I denote the n x n identity matrix, and let u #0 bé a column-vector in R". Show that the…

A: note : In the given formula it should be : λ1 = a + uTu , λ2 = a   As per the question we are given…

Q: Find the sum of the series. ∞ (−1)n 2nx2n n!   n = 0

A:

Q: Find n, if the ratio of the fifth term form the beginning to the 1 +$3) 43 fifth term from the end…

A:

Q: Find a, b, and n in the expansion of (a + b)" if the first three terms of the expansion are 729,…

A:

Q: Let p(x) = a + a₁x + a₂x² and g(x) = bo + b₁x + b₂x² be vectors in P₂ with (p, q) = aobo + a1b₁ +…

A:

Q: Consider two real systems, say Ax = b and Cy = d. If the two systems have the same nonempty solution…

A: To Determine: If the two systems Ax = b and Cy = d have the same nonempty solution set, then, is it…

Q: 3. Given r(t) = (sin 2t, cos 2t,cos² 2t) find T a) the equation of the tangent line to the r(t) at t…

A:

Q: In the United States, 40% of the population has brown eyes. If 15 people are randomly chosen, what…

A:

Q: 8]T T √r² +4

A:

Q: 12. (Exercise 16.22) Prove the third isomorphism theorem. At each major step in the proof, explain…

A:

Q: al pha =aFor a in S, we denote its ith com pon- equivalently, we have = (a¹; : : : ; an) This will…

A:

Q: Find the Laplace transform of f(t) = ( 2t-5t²)³

A:

Q: PEAK TRAM The Peak Tram in Hong Kong connects two terminals, one at the base of a mountain, and the…

A:

Q: Question 5. Let f: ZxZ→ ZxZ be the function defined by f(x, y) = (y-x, x+2y) Prove that f is not…

A:

Q: Prove that "C,(-1) [ +² +³ + 1¹²] Ź r=0 = 2" +2/2+1 cos (nπ/4), where i = √-1.

A:

Q: V. Numerical Differentiation - Find the slope of the function f(x) = (sin x)/x at x = TL.

A: The given problem is to find the slope of the given function at x=π. Given function f(x)= sinx/x.

Q: a) Find the third root of the equation Find the roots of the equation z3+1=0 and draw these roots.…

A: The given problem is to find the roots of the given equation and also to check the given function is…

Q: X1 2 1 NII 2 X2 X3 1 0 0 1 0 0 $1 1 82 2 -1 0 1 0 300 500 -1/201 2 3 1 2300 a) What is the maximum…

A:

Q: whose the family of curre intersecting at angle of find the isogonal trajectory of y = = Inx+C…

A:

Q: Let f: AB and 9: B→C be defined as follows: f(a) = 4a² +2 and g(b) = 26-7 Compute the following: (a)…

A: Let A=B=C=x|x is a real number Let f:A→B and g:B→C be defined as  fa=4a2+2andgb=2b-7 Hence…

Q: V. Numerical Differentiation - Find the slope of the function f(x) = (sin x)/x at x = TL.

A:

Q: V. Numerical Differentiation - Find the slope of the function f(x) = (sin x)/x at x = TL.

A: The given problem is to find the slope of the given function f(x)=sin(x)/x at x=π.

Q: Assume that the labour force is 16 workers, the capital stock is $6000, and output is $1700. If the…

A:

Q: If k and n are positive integers and sk= 1k + 2k + 3k + ... + nk, m then prove that Σm+¹C₁s, = (n +…

A:

Q: Integrating Factors Found by Inspection 5. (x²y²*² +ay)dx+(x™¹³y² +bx)dy=0. State the condition of…

A:

Q: 10 10 1 s+12 0

A:

Q: 13. Draw the graph G(V, E) where V = (a, b, c, d, e, f) and E = {ab, ad, bc, cd, cf, de, df).

A: Graph theory

Q: Find all the values of a such that the given series would converge. 6 (x)(n+1) (n +9) ∞ n=1 The…

A:

Q: Approximate the area under the curve y with 6 subdivisions. x³ from x = 1 to x = 4 using a Right…

A:

Q: Find a if the 17th and 18th terms of the expansion (2 + a)5⁰ are equal.

A:

Q: I need answer within 20 minutes please please with my best wishes

A:

Q: Q) Solve the following problems by using two phase method? 1-Max z= 5x1+12x2+4x3 ST 4x1-2x2+6x3=4…

A: The given problem is to find the linear programming problem with given constraints by using the two…

Q: -2.45-(-3.9).

A:

Q: Suppose that f(x, y) = x² − xy + y² = 5x + 5y with D = {(x, y) | 0 ≤ y ≤ x ≤ 5}. 1. The critical…

A: Given: fx, y=x2-xy+y2-5x+5y,  D=x, y|0≤y≤x≤5 To find:  1. The critical point of f(x, y).  2.…

Q: I have a very long rope of licorice: 93 inches long! If I cut it into 12 pieces, how long is each…

A:

Q: 6. Use a triple integral to find the volume of the solid between the plane z = 3 and the paraboloid…

A:

Q: Use the direct computation method to solve the following Fredholm integral equations

A: Given: Fredholm integral equation: u(x)=-11+9x+x3+x4-∫0120x-30t ut dtTo find: The solution of the…

Q: 2. Donald wishes to borrow $250,000, and he qualifies for a rate of 3.29%. for this loan if the term…

A: Donald borrow $250,000 at an interest rate of 3.29% for 30 year.

Q: 1. Using induction, prove that 2 (^(^^!) ) ² २ 2 3=1 J 3

A: The given problem is to prove the following identity by using the mathematical induction method.

Q: Problem I f(t) to F(s) Use tables 12.1 and 12.2 from the textbook to find: L { of cor wt} Use…

A:

Q: 02/05 The set of basis vectors {V₁, V2, V3} are augmented to form Matrix A. Which of the following…

A: