Squares Principle if you have n squares to place m objects and m>n then some square must be placed with at least two objects Use the box principle to answer the following a) show that if you have 5 points on the plane with integer coordinates there are two whose midpoint also has integer coordinates b) show that among 100 different positive integers it can be ensured that there are two of them whose sum is at least 199

Q: Let P1, P2, P3, .. , P78 be some coplanar points with k lines on the same plane. If exactly two line…

A: Given,  P1, P2,P3,...,P78 be some coplanar points with k lines on the same plane. If exactly…

Q: use Gauss Fordanmetrecd to Solbe the fellowsing setafeg Qe linear 2X+ -4x2 +6X3=5 A +3X2-783=; + 5…

A: Introduction: A system of linear equations can be solved using Gauss-Jordan elimination method. This…

Q: A plane is perpendicular to [x, y, z] = [3, -30, 24] + s[2, 4, -2] and contains the point…

A: Step 1:​Plane is perpendicular to [x,y,z]=[3,−30,24]+s[2,4,−2]Direction of Line…

Q: Find two examples for equivalet norms on three dimensional real space R³. .

A: To take two vectors whose norms are the same.

Q: II. The male division Male Data in inches 68 65.5 68.1 65.3 72.5 65.5 65.4 72 71.2 73.2 67.7 73.5…

A: Given that, n=32. The formula for mean and standard deviation is         mean=x¯=∑xin       standard…

Q: Let 7 -7 2 -2 -5 %3D - 3 -2 9. -8 a) Find the dimension of the row space ofA. b) Find the dimension…

A: The given matrix,A=117-72-2-565-3-25409-8

Q: Write a scalar equation of each plane. a) [x, y, z] = [2, -5, 4] + s[2, -3, −2] + t[7, -3, 5] b) [x,…

A: Since you have posted a question with multiple subparts, so we will solve only the first three…

Q: 6 Find the minimum of –x + 2y on the feasible set given by x 2 0, x5 4, y 2 2, and x+y24. a) 0 b) 2…

A: We graph x≥0, x≤4, y≥2 and x+y≥4 using a graphing calculator.

Q: Let a = (-3, 0, 4) and 6 = (0,4,-4). Find the projection of 5 onto ā. proj₁ = 25

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Q: 5) Again let Universe U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. Let S = {0, 1, 2}, T = {1,4}, R = {2, 4,…

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Q: Solution set of en eous write the the fallowing homogensaus aystem in pasmetaic fom fosm Xi +3x2…

A: The system of equation is given as x1+3x2-5x3 = 0x1+4x2-8x3 = 0-3x1-7x2+9x3 = 0 Corresponding…

Q: Initial Post Prompt Let 5 0 3 Include the following in your initial post: Justify all of your…

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Q: Let A € Rmxn and suppose that the rank of A is m where m is less than or equal to n and be Rm.…

A: Given: We are given a matrix A of size m×n with rank m where m≤n, a vector b of length m×1, and a…

Q: V = {ax² + bx + 3|a, b ≤ R} ≤ P2.

A: Given: V=ax2+bx+3 | a, b∈ℝ⊂ℙ2 To write: The given set as span of minimum number of vectors.

Q: Why is the set {91 +124t² - 61t³, 66 − 58t +93t², 22 + 248t — 87t² } not a basis for P3(R)? Select…

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Q: Below are four coordinate axes for 3-space, labeled I, II, III, and IV. Which sets of axes adhere to…

A: Once the x- and y-axes are specified, they determine the line along which the z-axis should lie, but…

Q: Find the distance from y to the plane in R³ spanned by the set (U₁, U₂} 6 - 2 4 y = -9 a. b. C. 43₁…

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Q: Does there exist a pair of orthogonal Latin squares of order 54? Explain why or why not?

A:

Q: • A is in RREF ● ● -689 Let A Fill in the blanks such that A has all of the following properties.…

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Q: Let a = (-3, 0, 4) and 6 = (0,4,-4). Find the projection of 5 onto ā. proj₁ = 25

A:

Q: 6. If A has m members and B has n members, prove that A x B has mn members 7. Sketch each of the…

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Q: 5. Let S be the set of all points (x11, X12, X13, X22, x23; X33) E K® such that the matrix x11 *12…

A: The objective is to determine if the set S is convex or not, where  S is set of all points…

Q: Q2. Let X = {a, b, c, d, m, n}, T = {ø, X, {c}, {m, n}, {a, b, c, d}, {c, m, n}}. and Y = {b, c, m}…

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

Q: seeas to germinate if they are near rockK music that is continuousiy playing compared to being near…

A: Given: Sample sizes: n1=51n2=40 Sample means: X¯1=22X¯2=19 Standard deviations: s1=11s2=5…

Q: min 3x - 2x2 3x₁ + x₂ ≤ 12 3x - 2x2 2,32 2x₂ - 23 21 22 23 20 7 (1 12

A: The given linear programming problem is given by Min 3x1-2x2subject to…

Q: Explain why the two planes P₁: =(2,5,3)+(2,-1,-3) +(1,0,-1), s,/€ R, and P',: 7=(4,4,0)…

A: