Let a₁ = B , a₂ = 圓 and a3 = The set {a₁, a2, a3} will span R³ unless h = 7.5 (If there are no values of h that make the set fail to span, enter "NONE". If the set fails to span for all values of h enter "ALL".)

Q: Which of the following sets is a linearly independent set? a. (1,2),(5,10) b. (1,2),(5,8) c.…

A: Linearly independent and dependent set

Q: The geometric object in 3-space represented by the equation (x +y +z)^2 = 81 is O a. the line…

A: This is quadratic equation.  When this quadratic expression can be factored in two linear factors…

Q: Let a1 = [-2  h], and a2 = [10  -20] The set {a1,a2} will span R3 unless h

A:

Q: If P = {a, b, c} and Q = {r}, form the sets P × Q and Q × P. Are these two products equal?

A: P × Q = {a,b,c} × {r} = {(a,r) , (b,r) , (c,r) } Q × P= {r} × {a,b,c} = { (r,a) , (r,b) , (r,c) }

Q: 2. If A = {a,b,c}, B = {1,2,3}, C = {x}, and D = 0, list all of th the following sets. (a) Ax B (c)…

A:

Q: Use graphs to find set. (-3, 0)∩[-1, 2]

A: The given sets are We need to find the intersection of these two sets using graphs.

Q: 13. Find the Cartesian product A x B of the sets A = {12, 9, 10} and B = {14,4}

A:

Q: Find the value of a for which 4 1 is in the set 2 H = span -3 4 -2 a =

A:

Q: h --0-8-0 = and a3 = -4 -3 The set {a₁, a2, a3} will span R³ unless h Let a₁ = -127 4 -17 -3

A: Given:

Q: Let a₁ = -3 h -2 a₂ = -6 1 , and a3 = -8 20 The set {a₁, a2, a3}| will span R³ unless h = 19 (If…

A:

Q: Determine the equation of the set of all points equidistant from the points A(1,0, 1) and B(2,2, 2).…

A: Given, The points A(1,0,1) and B(2,2,2). Point C is equidistant from two points A and B if the…

Q: Use graph to find  set. (-2, 1] ∪ [-1, 3)

A: Given set is  (-2, 1] ∪ [-1, 3) The graph for the given set is as shown

Q: If #: $ a,b,c} which of these celations are a funchion? Emplain, cab) CS

A: Solution : Given :    A= {a, b, c}  Set of relations are      a)    { (a, b), (b, c), (c, c) }…

Q: Find the value of a for which 4 is in the set -1 H= span -3 4 -2 a = 15

A:

Q: N repteseated by Determin, the lorus 1z -3 -|2+31 =4' %3D

A: Given that : b) argz+1z=π4That can be written as,argz+1-arg(z) =π4Let substitute z =…

Q: Indicate whether the two sets are equal. D = {x: x is a natural number less than 3}, E = {1, 2, 3}

A:

Q: Find the power set of A= {{ }, 1, {b}, 4 } and write how many relations can be defined on A

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Q: Use any method you choose to show that An (B UC) = A U B n C, when A, B, and C are sets.

A:

Q: explain why the entire real line R is both open and closed.

A: In standard topology, the entire real line (R) is considered both open and closed. Let's break down…

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A: Given that  be a linear combination of .

Q: Find the intersection of the sets. {a, b, c, d}∩∅

A: Given sets are {a, b, c, d} and an empty set ϕ

Q: (2b) Let A and B be sets. Prove that A – B is disjoint from A n BC LA O BE

A: The set A∩B is defined as A∩B=x|x∈A and x∈B The set A-B is defined as A-B=x|x∈A and x∉B Two sets are…

Q: Find the number of relations from the set A {a, b, c} to the set B = {1,3}

A: