Let x, y, z be (non-zero) vectors and suppose w = 12x + 18y + 4z...

Let x, y, z be (non-zero) vectors and suppose w = 12x + 18y + 4z

If z = − 2x − 3y, then w = 4x + 6y

Using the calculation above, mark the statements below that must be true.

A. Span(w, x, y) = Span(w, y)
B. Span(x, y, z) = Span(w, z)
C. Span(w, x, z) = Span(x, y)
D. Span(w, z) = Span(y, z)
E. Span(x, z) = Span(x, y, z)

Solutions

Expert Solution

Colby Messinger answered 1 year ago

Next > < Previous

Related Solutions

2) Let v, w, and x be vectors in Rn. a) If v is the zero...

2) Let v, w, and x be vectors in Rn. a) If v is the zero vector, what geometric object represents all linear combinations of v? b) Same question as a), except now for a nonzero v. c) Same question as a) except now for nonzero vectors v and w (be care- ful!). d) Same question as a) except now for nonzero vectors v, w, and x (be extra careful!).

Proposition 8.59. Suppose that X, Y, W, Z, A, B are sets. Let f : X...

Proposition 8.59. Suppose that X, Y, W, Z, A, B are sets. Let f : X → Y , W ⊆ X, Z ⊆ X, A ⊆ Y , and B ⊆ Y . Then the following are true: prove the following ? (1) f(W ∩ Z) ⊆ f(W) ∩ f(Z). (2) f(W ∪ Z) = f(W) ∪ f(Z). (3) f−1(A ∩ B) ⊆ f−1(A) ∪ f−1(B) 4) f−1(A ∪ B) = f−1(A) ∪ f−1(B). (5) X−f−1(A)⊆f−1(Y −A). (6) W...

Let X, Y ⊂ Z and x, y ∈ Z Let A = (X\{x}) ∪ {x}....

Let X, Y ⊂ Z and x, y ∈ Z Let A = (X\{x}) ∪ {x}. a) Prove or disprove: A ⊆ X b) Prove or disprove: X ⊆ A c) Prove or disprove: P(X ∪ Y ) ⊆ P(X) ∪ P(Y ) ∪ P(X ∩ Y ) d) Prove or disprove: P(X) ∪ P(Y ) ∪ P(X ∩ Y ) ⊆ P(X ∪ Y )

If X, Y and Z are three arbitrary vectors, prove these identities: a. (X×Y).Z = X.(Y×Z)...

If X, Y and Z are three arbitrary vectors, prove these identities: a. (X×Y).Z = X.(Y×Z) b. X×(Y×Z) = (X.Z)Y – (X.Y)Z c. X.(Y×Z) = -Y.(X×Z)

Please explain this prolog code line by line. union([X|Y],Z,W) :- member(X,Z), union(Y,Z,W). union([X|Y],Z,[X|W]) :- \+ member(X,Z),...

Please explain this prolog code line by line. union([X|Y],Z,W) :- member(X,Z), union(Y,Z,W). union([X|Y],Z,[X|W]) :- \+ member(X,Z), union(Y,Z,W). union([],Z,Z).

The curried version of let f (x,y,z) = (x,(y,z)) is let f (x,(y,z)) = (x,(y,z)) Just...

The curried version of let f (x,y,z) = (x,(y,z)) is let f (x,(y,z)) = (x,(y,z)) Just f (because f is already curried) let f x y z = (x,(y,z)) let f x y z = x (y z)

Given two planes 2x - y + z = 7 and x + 3y - 4z...

Given two planes 2x - y + z = 7 and x + 3y - 4z = 1. (a) Give an orthogonal vector to each plane. (b) Do the planes intersect? Why or why not? (c) If they intersect, find the parametric equation of the intersection line, if not, find the distance of both planes.

. (a) Let a and b be two non-zero vectors with a common initial point 0...

. (a) Let a and b be two non-zero vectors with a common initial point 0 and whose directions are inclined at an angle O. Define the vector product of a and b. (b) The position vectors of the points A, B, C and D are 2i + j + 3k, 4i - j + 7k, -i - 2j - 2k and 2i - 5j + k respectively. Show that the lines AB and CD are skew. Find a direction...

5. Let X, Y and Z be sets. Let f : X ! Y and g...

5. Let X, Y and Z be sets. Let f : X ! Y and g : Y ! Z functions. (a) (3 Pts.) Show that if g f is an injective function, then f is an injective function. (b) (2 Pts.) Find examples of sets X, Y and Z and functions f : X ! Y and g : Y ! Z such that g f is injective but g is not injective. (c) (3 Pts.) Show that if...

Let W be a subspace of R^n and suppose that v1,v2,w1,w2,w3 are vectors in W. Suppose...

Let W be a subspace of R^n and suppose that v1,v2,w1,w2,w3 are vectors in W. Suppose that v1; v2 are linearly independent and that w1;w2;w3 span W. (a) If dimW = 3 prove that there is a vector in W that is not equal to a linear combination of v1 and v2. (b) If w3 is a linear combination of w1 and w2 prove that w1 and w2 span W. (c) If w3 is a linear combination of w1 and...

Subjects