Let V be a vector space of finite dimension n over a field F , and let U be a subspace of V of dimension n − 1. If W is a subspace of V not contained in U , show that dim(U ∩ W ) = dim(W ) − 1.

Q: 1. Consider the function f(x) = x² - sin(x) -0.5. Plot the graph of the function in the interval [0,…

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

Q: 58. Which function has Maclaurin series .(-1)k -(x – 3)k? 3k+1 k=0 For which values of x is the…

A: To find: The function f(x) for which the expansion is ∑k=0∞(-1)k3k+1(x-3)k, and the values of x for…

Q: he relati

A:

Q: (x - y - 1) dx - (4y + x) dy = 0 Give the: a. homogeneity b. degree c. reducible homogeneous…

A:

Q: T(n) = 2T(n − 1) + 1, T(0) = 1. Use the iteration method to find a ☺() evaluation for T(n).

A: T(n) =2n+2n-1+2n-2+2n-3+...+22+21+1

Q: Evaluate the following, assuming, h 1. A(x³ - 3x² - 5x+8) 2. 4²(x³ +7x² + 4x + 10) 3. A² (x-4)(x −…

A:

Q: Outside temperature is 16°C @ 12:00 pre @12:00 pm on object is 34.5 °C @ 1:00 pmr save object is…

A:

Q: hyperbolic geometry, why would the fourth angle of a parallelogram with 3 right angles be acute and…

A:

Q: Given a 4x4 matrix as follows: Row 1 (1,4,3,-6); Row 2 (4,-21,43,64); Row 3 (7,2,10,1), Row 4…

A: The given matrix is as follows ; A = 143-64-2143647210191721-28 We have to find the determinant of…

Q: An economy consists of coal, electric, and steel sectors. For each $1.00 of output, the coal sector…

A:

Q: Find the distance between the points p1and P2. P1 =(-4, -3); P2 =(6, 2)

A: We have to find the distance between the points P1 and P2. We have to use the distance formula for…

Q: Problem 25. Suppose yı (x), y2(x), and y3(x) are three different functions of x. The vector space…

A:

Q: A tank is initially filled to capacity with 250 L pure water. At t=0, brine containing 2 g/L salt is…

A:

Q: Give one ORIGINAL example (problem-solving) Given: ● Solution Answer 1. INDUCTION AND DEDUCTION

A: Given: "Induction and deduction" approachWe need to give an example that explains both approaches…

Q: Representative matrix and constant system of linear equations Ax = b, where X= [X1 X2 X3]T 5 7 60 4…

A:

Q: Find Lim (x² (X, Y) → (0, 0) + Y²) Log (x² + Y²)

A: To find the limit  lim(x,y)→(0,0)(x2+y2)log(x2+y2)

Q: Find the differential equations of the following primitives by eliminating the arbitrary constants.…

A: We know that the rate of change of a function with respect to a variable is called the derivative of…

Q: S (-1,3] U [5, 6) Ø {x ln(x) x>0} inf (S) sup(S)

A:

Q: 3. xy³dx + ex²dy = 0

A:

Q: Give an explicit increasing linear bijection from the interval (a, b] (a < b) to (0, 1]. i.e. your…

A:

Q: The region bounded by the curves y² = 8x and 2y = x³ is revolved about the line y-axis. Find the…

A: Given the curves y2=8x, 2y=x3 revolved about the line y-axis.

Q: What is the homogeneity and degree of the following differential equation?  (x + y + 1) dx + (2x +…

A:

Q: Question 1 If H = (x - y)ax + (x² + zy)ay + 5yzaz Evaluate the line integral along the contour of…

A:

Q: +...+ + ਸ = 2 - ਨੂੰ ਜ 10. 1++++ 11. A + + + 7 + ··· +3 || 3 2 2 (3).

A:

Q: A train travels along a set of tracks according to the function s(t)=r-121² +45r+ 4 for r 20, where…

A:

Q: The function f in the figure satisfies lim f(x) = 4. Determine the maximum value of 8>0 satisfying…

A: If x&lt;k and k is a constant, then it can be written that -k&lt;x&lt;k.

Q: Eliminate the arbitrary constants of the following

A: Since you have posted multiple questions and we can answer one question. So, answered the first…

Q: II. Obtain the particular solution of the following differential equations 4. (3x²2y²)y= 2xy; when…

A:

Q: You plan to sell cupcakes to raise funds. A bakery charges you ₱15.00 for the first 100 cupcakes.…

A: Hint: Suppose the number of cup cakes is x. and f(x)= Charges It is given that charges per cup cakes…

Q: Suppose someone says that the price of a share of Google stock is a function of time. Translate this…

A: Functions is a mathematical term denoting dependence of a certain variable to another.Time here is…

Q: a) 3log2 16 b) log, 2+log, 6-log, 4

A:

Q: Given an effective daily rate j365 = 0.01877%, find the equivalent effective bi-weekly rate. a.…

A: Given an effective daily rate j365=0.01877% We have to find an equivalent bi-weekly rate.

Q: 1. Determine the magnitude of the resultant of the two forces shown and its direction measured from…

A: A vector is a quantity that has magnitude and direction and that is commonly represented by a…

Q: 6) Find д at OP V, given that PV = nRT; (n and R are cons onstant)

A:

Q: Question 20 If R¹ = {(2,4), (5,7), (8,8) }, then which of the following represents the range ofR?…

A: Note: Hi! Thank you for your question. As per the guideline we can solve one question at a time in…

Q: Let function g (x,y) = 3x + y ln y sin (1 − x) - Assume z as function differentiable at x and y…

A:

Q: 9. The number of Internet users in a country for various years are shown in the table below. Let n…

A: Given: The number of internet users in a country for various are shown in the table. Year Number…

Q: For each of the following functions f(x) (x € R²), describe the sets = { x | f(x) ≤ 4} and show, by…

A: As per guidelines, I can only first three subparts of the question ( parts (a), (b), (c))

Q: Construct a truth table for the given statement. b~ A (bv d~) V P TT T b F EL. T FF v de bv dr bN bN…

A: Introduction: A table that displays the truth value of each component statement in a compound…

Q: 3. Three difference equations of the form Pn= f(Pn-1) are given below. For each graph y = f(x) and y…

A: We are given three difference equations of the form Pn=f(Pn-1)  and P0=0.8.  We need to draw cobweb…

Q: Proxx BA (UxAx) = Ux (BO) Ax

A:

Q: It says that the answer is wrong. Do you happen to know the actual solution?

A: let the investment on stock ball is x let the investment on stock coff is y according to question,…

Q: -2 2 B-8-8 -2 Compute the distance d from y to the subspace of R¹ spanned by v₁ and v2. Let y = -1 5…

A:

Q: (3+ y + 2y²sin²x) dx + (x + 2xy-ysin2x)dy = 0; when x = 4, y = 1

A:

Q: for Y^2 = x^3 + 4x + 3 (mod7) show that points on the curve are: show that (1,1) + (5,1) = (3,0)…

A:

Q: Show that CC R" is closed if and only if bdry (C) C C.

A:

Q: (a) Of the 7 new programmers hired by a software company, 4 will work on web applications, 2 will…

A: It is given that, 7 new programmers hired by a software company out of which, 4 will work on web…

Q: A hardcover book sells for 1995 php in an online bookstore. The royalties paid to the author is…

A:

Q: Must solve both the questions. Don't solve only one. Solve both or else skip it for others.

A:

Q: Use the inner product = = f(x)g(x)da in the vector space Cº[0, 1] to find the orthogonal projection…

A: Given,         f(x)=2x2+4,     g(x)=x-12 and  h(x)=1. To find                  projvf=?.