Let G a graph of order 8 with V (G) = {v1, v2, . . ....

Let G a graph of order 8 with V (G) = {v1, v2, . . . , v8} such that deg vi = i for 1 ≤ i ≤ 7. What is deg v8? Justify your answer.

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Expert Solution

Colby Messinger answered 2 years ago

(a) If V1,V2⊂V show that (V2^⊥)⊂(V1^⊥) implies V1⊂V2 (b) If V1,V2⊂V , show that (V1+V2)^⊥=(V1^⊥)∩(V2^⊥) where...

(a) If V1,V2⊂V show that (V2^⊥)⊂(V1^⊥) implies V1⊂V2 (b) If V1,V2⊂V , show that (V1+V2)^⊥=(V1^⊥)∩(V2^⊥) where we write V1+V2 to be the subspace of V spanned by V1 and V2 .

Let {v1, v2, v3} be a basis for a vector space V , and suppose that...

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If G = (V, E) is a graph and x ∈ V , let G \...

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v1=[0,1,4] v2=[-4,-5,7] v3=[14,10,8] b=[16,18,19]. Let v1,v2, and v3 be three nonzero vectors in R3. Suppose v2...

v1=[0,1,4] v2=[-4,-5,7] v3=[14,10,8] b=[16,18,19]. Let v1,v2, and v3 be three nonzero vectors in R3. Suppose v2 is not a scalar multiple of either v1 or v3 and v3 is not a scalar multiple of either v1 or v2. Does it follow that every vector in R3 is in span{v1,v2,v3}?

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let l be the linear transformation from a vector space V where ker(L)=0 if { v1,v2,v3}...

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Let v1 = [-0.5 , v2 = [0.5 , and v3 = [-0.5 -0.5 -0.5 0.5 0.5 0.5 0.5 -0.5] 0.5] 0.5] Find a vector v4 in R4 such that the vectors v1, v2, v3, and v4 are orthonormal.

16. Which of the following statements is false? (a) Let S = {v1, v2, . ....

16. Which of the following statements is false? (a) Let S = {v1, v2, . . . , vm} be a subset of a vector space V with dim(V) = n. If m > n, then S is linearly dependent. (b) If A is an m × n matrix, then dim Nul A = n. (c) If B is a basis for some finite-dimensional vector space W, then the change of coordinates matrix PB is always invertible. (d) dim(R17) =...

if {v1,v2,v3} is a linearly independent set of vectors, then {v1,v2,v3,v4} is too.

Let G = (V, E) be a directed graph, with source s ∈ V, sink t...

Let G = (V, E) be a directed graph, with source s ∈ V, sink t ∈ V, and nonnegative edge capacities {ce}. Give a polynomial-time algorithm to decide whether G has a unique minimum s-t cut (i.e., an s-t of capacity strictly less than that of all other s-t cuts).

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