By using the method of least squares, find the best line through the points: (2,-3), (-2,0), (1,-1). Step 1. The general equation of a line is co + C₁ = y. Plugging the data points into this formula gives a matrix equation Ac = y. = Step 2. The matrix equation Ac = y has no solution, so instead we use the normal equation A™A ĉ=A¹y ATA = A¹y = Step 3. Solving the normal equation gives the answer Ĉ= which corresponds to the formula y = Analysis. Compute the predicted y values: y = Ac. ŷ = Compute the error vector: e = y - y. e= Compute the total error: SSE = e² + e +e3. SSE =

Q: III. Let S be the quadric with equation 4x² - (y - 3)² + 4z² = 4. a. What type of quadric is S? Find…

A: 4x2 - (y-3)2 + 4z2 = 4 (C) The quadric S can also be identified as a surface of revolution.

Q: 6. Show that a compact metric space X is locally compact.

A: The given problem is related with metric space. We have to show that a compact metric space X is…

Q: A forest has a population of lynx and a population of rabbits. Let a represent the number of lynx…

A: Solution: x'=dxdt=-0.25x+y  .....1y'=dydt=-x+4y  .....2B.C.S: x0=0 and  y0=1From equation 1  and 2…

Q: A company determines that its total cost, in thousands of 3x rands, for producing x items is C =…

A:

Q: Given the formula, S n =a 1-r^ n 1-r what is the sum of the first nine terms of the geometric series…

A: Note: The geometric series has to be 324, -108, 36, -12,....., Otherwise there will be no common…

Q: Suppose we want to choose 7 colors, without replacement, from 10 distinct colors. (a) If the order…

A:

Q: 14. Write the given system of differential equation as a matrix equation X' = AX. dx = 2x + 3y, dt…

A: System of differential equations: A finite set of differential equations with one independent…

Q: (3) The solution of the following problem for the wave equation on the entire real-line: that=Uz…

A:

Q: 4. Which of the following subsets of R³ constitute a subspace of R³? [Here, x = (₁, §2, §3).] (a)…

A:

Q: Let S be the quadric with equation 4x² − (y - 3)² + 4z² = 4. What type of quadric is S? Find an…

A: The quadric equation given is as follows: 4x2-y-32+4z2=4 (a) Rearrange the above equation.…

Q: Consider the polar curves C₁ r = 2 cos 0 and C₂: r = 2 cos 30, and let R be the shaded region as…

A: Same point can be expressed in polar coordinates in various ways.

Q: A graph of y = f(x) is shown. In the same coordinate system, sketch a graph of the derivative…

A: Here is the graph of y=fx as shown below,

Q: Find Vector A and B such that A is parallel to , B is perpendicular to and A + B =

A: Any vector parallel to the vector: a, b, c is ka, kb, kc, where k is a constant. If two vectors are…

Q: a. Which of the following surface graphs represents f(x,y) = y²? OA.

A: Given, the surface                           z=f(x, y)=y2

Q: prove that (z(square root 2,+,×)) is integral domain.

A: We have , ℤ2   =  a + b2 / a , b ∈ ℤ We need to show that  , ℤ2 is integral domain. We know that , a…

Q: Find the length of the curve. Hand written plzz √2ti + etj + etk, 0 ≤t≤ 3

A:

Q: aving 3m2 of aluminu

A: Given Having 3m2 of aluminum foil at your disposal, you want to build a rectangular box with a lid,…

Q: E be a Euclidean space of dimension (E(1, f)) = dim(Ker (f- id)), then s minimal.

A:

Q: QUESTION 2: Find the approximation for the integral 4 1 S₁ 2x² dx, when applying: the Trapezoidal…

A:

Q: A van costs $25,000 and has an expected life of 6 years, with a salvage value (Residual Value) of…

A: Given that: Actual cost of the van = $25,000 Expected life = 6 years Salvage value = $1,500 To…

Q: 9) If f(z) = u - iv is analytic in the z-plane, then the C-R equations satisfied by it's real and L…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Mrs. Cruz asked her 30 students who among their mother, father, or sibling will attend the quarterly…

A: Let us consider A , B, C be three sets then  Some Properties of the set theory n(only…

Q: 0 < x < 1 1< <2 2 <지

A:

Q: 18. Figure F is graphed. Transform figure F using the rule (x,y) → (x-8,-y). YA 10 8

A: Introduction: Graph transformation is the process of modifying an existing graph or graphed equation…

Q: 3. Determine whether the sequence converges or diverges. If it converges, find the limit. an 21+3n =

A: Solution:an=21+3nnOn rewriting this equation, we get 21+3nn which turns into [21n(23)]Here 23=8 that…

Q: Solve the system of differential equations. -17 x' = [3¹] 15 x₁ (0) = 8, x₂(0) = -8 x₁(t) = x₂(t) =

A:

Q: (2) If c(z) ≥ 0 for all z = [0, 1], then a function minimizes J(v), that is, J(u) = inf J(v), with…

A:

Q: B. SOLUTION OF HOMOGENEOUS SYSTEM GIVEN: 1 -13 -1 4 0 2 -2 1 100 10-20 1 0 A= 0011-10

A:

Q: Given a Euclidean space E there is an orthonormal basis t. this basis is a diagonal mat λ₁

A:

Q: Assume that the Taylor series centred at x = 0 of a function f(x) is Σo anx" Let g(x) = f(x³).…

A: The expansion f(x) is f(x)=∑n=0∞anxn Here a0=1, a2=2, a2=3, a4=4 Since  a0=1⇒f(0)=1…

Q: 1) f(x) = zarn 7:0 3-X ·r

A: Solution:-

Q: 1. If x=27-3k and y = 7+57-4k, express each of the following in terms of i, j, k a) 5x-2y

A:

Q: y- y' cos x = y² cos x (1 - sin x)

A:

Q: Find the value of x. X+ 5-

A: Incentre is a point that lies in a triangle. The bisector os all the angles of a triangle meets at…

Q: Sketch f(t) and find the Laplace Transformation of the following functions t, 0 < t < 1 i) f(t) =…

A:

Q: Consider the vector-valued function Ŕ(t) = a. Find the domain of R. b. Determine if R is continuous…

A:

Q: III. Let S be the quadric with equation 4x² − (y - 3)² + 4z² = 4. a. What type of quadric is S? Find…

A: Since you posted multiple question, we will solve first question for you. Kindly repost other…

Q: - 23 + 132-та -3 наха +2+12 (; +ана - -7³ 2 э

A: We have to write the given expression -λ3+13λ-12 as a product of linear factors. For this, we have…

Q: Let f C D be a function, with C being the domain and D being the codomain. Show that for any C₁, C₂…

A: Solution: Let  x ∈ fc1∩c2⇒∃  y∈ c1∩c2such that fy=x⇒y∈ c1 and y∈ c2⇒fy ∈ fc1 and fy ∈ fc2⇒fy ∈ fc1∩…

Q: Activity 1. Find the lower and upper triangular matrix of 14 D -2 7 using Cholesky Method L = -2 71…

A: A symmetric positive definite matrix: A can be decomposed into the product of an upper and lower…

Q: Separation of variables The lateral radiation of heat from a bar of length L insulted at both ends…

A:

Q: 2. By changing to cylindrical coordinate, evaluate So 1-x²1542x² dzdydx

A: Introduction: Sometimes, a triple integral given in the rectangular coordinate system is very…

Q: using the following: A(1, 0, -1), B(1, 7, 2), C(2, 4, -1), D(0, 3, 2) a) find the area of the…

A:

Q: Find the daigram only for the equation  z =x^2+y+cos(x^2)+siny

A: z=x2+y+cos(x2)+siny

Q: 2. Using both trapezoidal and Simpson rule, find the approximate values for the integral In(tan…

A: We need to find the approximate values of ∫π4π2ln(tan(x))dx using trapezoidal and Simpson rule given…

Q: Provide all answers to four (4) decimal places. Applying the Gauss-Seidel method in solving the…

A:

Q: Find the Laurent expansion of g(z) = (2-1)/[23+322 +22] in i) 0 < 2 <1 ii) 3<|z| 0<z +2 <1 E

A: As per guidelines we experts are allowed to solve three sub-parts at a time. Please reupload the…

Q: Let A, B₁, B, be sets. Using induction on 2, prove the following statements: (a) AU (B₁n B₂n CHICA…

A:

Q: Let f be a function which has an inverse and let f(-1) = 2. If Q is the surface of revolution…

A: As per the question we are given an invertible function f such that f(-1) = 2 And Q is the surface…

Q: identify and sketch the graph z = √(4 - y^2) in R^3

A: Given z=4-y2