Suppose Smokey the Bear is camping on the Olympic peninsula and a fly gets trapped in his tent. Let the tent be represented by the polyhedron P with vertices (0, 0, 0), (0, 1, 0), (1, 1, 0), (1, 0, 0), (0, 1/2, 1),(1, 1/2, 1) and let the position of the fly be represented by the random vector (X, Y, Z). Assume that the position of the fly is uniformly randomly distributed within P. 1. Compute the marginal p.d.f. of X, Y, and Z individually 2. Are X, Y, Z independent? 3. Are X and Y independent? Are X and Z independent? Are Y and Z independent?

Q: 4. Prove that the vectors a= (1,1,1); b-(1,-1,0) and e-(-1,-1.2) are orthogonal to each other! 5.…

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Q: 2. Determine whether the vectors v, are orthonormal. If not, normalize them to produce an…

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Q: (Section 5.3) i. Show that the vectors v₁ = (1, 2, 3, 4), №₂ = (0, 1, 0, −1), and v3 = (1,3,3,3)…

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Q: 4. Given 3 points: A(2, 1, 1), B(2, 2, 2), and C(4, 2, 2), compute the normal vector for the…

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Q: 1. Two matrix vectors a and b are given as a = -0--0 and b Find (alb).

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Q: Find the projection of u = onto v = .

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Q: Show that the three points (x1, y1), (x2, y2), and (x3, y3) in a plane are collinear if and only if…

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Q: 7. Given =(-7,-4) and w=(8,-2), find the following for problems 6 and 7. Make sure you use proper…

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Q: Let {V₁,..., Vk} be an orthogonal set in R". Which of the following are true? Select one or more: ✔…

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Q: For what values of m and n are vectors [m,n,1], [2,1,3] and [2,1,1] coplanar?

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Q: Is v = |1a vector in the span of S = }|2| Use Gaussian elimination to support your answer.

A: To check v=111 a vector in a span of S=123, 012, -201 or not.

Q: Pick two random vectors in R³ (no zeros - few repeated numbers) and call them u and 7. Compute the…

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Q: 10 -2 Let A = 0 3 -4 and b= 5 . Denote the columns of A by a, , a2, a3, and let W = Span {aq, a2,…

A: Given A=10-203-2-462 and b=152 Column of A denoted by a1, a2, a3 W=spana1,a2,a3

Q: Can you please help me with question 9 please.

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Q: Suppose V={v1,v2,...,vn} is a set of nonzero vectors, and let                    x= a1v1 + a2v2…

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.