Solve the following equations and check your answers.

Q: 11. Find the eigenvalues and eigenvectors of the matrix: O 5.

A: Make the characteristic equation and then go ahead

Q: 4. If f (x, y) = sin(x)+e*y, find Vf (x, y).

A: Use gradient concept

Q: Determine whether P = and Q = are orthogonal vectors. If W = and V =, compute V x W. If W = and V =,…

A: Explanation of the answer is as follows

Q: 15sin (t), y 8cos (t) 3. Eliminate the parameter to find a Cartesian equation of the curve: x =

A:

Q: log 3 (x + 1) + log (y – 2) = 2 log3 (y) – log3 (r + 1) = 0

A: Given equation - log3(x+1) + log3(y-2) = 2log3x+1y-2 = 2                            log(a×b) =…

Q: Which number is a rational number? A. V3 B. V36 C. V7 D. Write 0. 15 as a simplified fraction. Show…

A:

Q: 1. The line passes through (3,2) and has a slope of -2. * A. 2x + y = 4 B. 2x - y = 4 C. 2x + y = -4…

A:

Q: [3 0 07 6. Find the eigenvalues and eigenvectors of the matrix: 0 5 0 Lo 0 7.

A:

Q: Let X be the set of all real numbers in [0, 1] whose infinite decimal expansion does not contain a 2…

A: We need to prove that X is Lebesgue measurable. Before proving that, first, we need to know what…

Q: Olivia bought a television at a store that gave a 30 percent discount off its original price. The…

A: Since you have asked multiple questions, as per our company guidelines,  we will solve the first…

Q: Let f: RR be a Lebesgue measurable function. Prove hat there exists a Borel measurable function g: R…

A: Let f:ℝ→ℝ be a Lebesgue measurable function.

Q: Write the first five terms of the sequence with the given nth term. = sinl an a a3 as

A:

Q: A Jacobian matrix and an equilibrium are given. Determine if the equilibrium is locally stable,…

A:

Q: Let (N, F, P) be a probability space. If E₁, E2,..., En F are events, show that for all positive…

A: Given that Ω, F, ℙ be a probability space and E1, E2, . . ., En∈F are events.

Q: Let ECR. Show that E is Lebesgue measurable if and only if there exists a sequence of open sets…

A: Given information: Set E is a subset of ℝ. Statement 1: E is measurable. Statement 2: There is a…

Q: 12. Compute the following double integral over the indicated rectangle:S S230xy²dA, R = [2,4] ×…

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.