Let x,y,zx,y,z be (non-zero) vectors and suppose
w=10x+10y−4zw=10x+10y−4z.
If z=2x+2yz=2x+2y, then w=w= x+x+ yy.
Using the calculation...
Let x,y,zx,y,z be (non-zero) vectors and suppose
w=10x+10y−4zw=10x+10y−4z.
If z=2x+2yz=2x+2y, then w=w= x+x+ yy.
Using the calculation above, mark the statements below that must
be true.
A. Span(x, z) = Span(w, z)
B. Span(w, y, z) = Span(x, y)
C. Span(w, z) = Span(w, y)
D. Span(w, x) = Span(x, y, z)
E. Span(w, y) = Span(w, x, y)
proof with The following features: Trichotomy, Transitivity,
Connection compatibility, Compatibility with multiplication
1.∀x, y ∈ Q...
proof with The following features: Trichotomy, Transitivity,
Connection compatibility, Compatibility with multiplication
1.∀x, y ∈ Q xy>0 ⇐⇒ (y > 0 and x > 0) or ( 0 > y and
0 > x)
2.∀ x ∈ Q x^2 > 0 ⇐⇒ x is not equal to 0
3. ∀ x, y, z, w∈ Q (x < y) ∧(z < w) ⇒ x+z < y+w
4.∀x, y, z, w∈ Q (0 < x < y) ∧(0 < z <
w)...
Suppose ?(?,?)=??(1−10?−10?) f ( x , y ) = x y ( 1 − 10 x...
Suppose ?(?,?)=??(1−10?−10?) f ( x , y ) = x y ( 1 − 10 x − 10 y
) . ?(?,?) f ( x , y ) has 4 critical points. List them in
increasing lexographic order. By that we mean that (x, y) comes
before (z, w) if ?<? x < z or if ?=? x = z and ?<? y <
w . Also, describe the type of critical point by typing MA if it is
a...
Consider permutations of the 26-character lowercase alphabet
Σ={a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z}.
In how many of these permutations do
a,b,c...
Consider permutations of the 26-character lowercase alphabet
Σ={a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z}.
In how many of these permutations do
a,b,c occur consecutively and in that
order?
In how many of these permutations does a appear before
b and b appear before c?
1. Write the following sets in list form. (For example, {x | x
∈N,1 ≤ x...
1. Write the following sets in list form. (For example, {x | x
∈N,1 ≤ x < 6} would be {1,2,3,4,5}.) (a) {a | a ∈Z,a2 ≤ 1}. (b)
{b2 | b ∈Z,−2 ≤ b ≤ 2} (c) {c | c2 −4c−5 = 0}. (d) {d | d ∈R,d2
< 0}.
2. Let S be the set {1,2,{1,3},{2}}. Answer true or false: (a) 1
∈ S. (b) {2}⊆ S. (c) 3 ∈ S. (d) {1,3}∈ S. (e) {1,2}∈ S (f)...
1. Suppose that x, y, z, and w are int variables. What is stored
in x,...
1. Suppose that x, y, z, and w are int variables. What is stored
in x, y, z, and w after the following statements execute? (3,
6)
x = 9;
y = x - 4;
z = (y + 7) % 6;
w = (x * z) / y - 3;
z = w + (x - y + 2) % x)
Recall that a subset A (of N, Z, Q) is called downward closed
when x ∈...
Recall that a subset A (of N, Z, Q) is called downward closed
when x ∈ A and y < x implies y ∈ A. Suppose that A is a downward
closed subset of Z, and consider the subsets
B = {x + 1 ∈ Z | (∃y ∈ A).x2 ≤ y} C = {x − 1 ∈ Z | (∃y ∈ A).x
< y2 }
For each of B, C, determine whether it is downward closed in Z.
Explain...