Let w, x, y, z be vectors and suppose z = -x + 3y and w = 3x – y+ 3z. Mark the statements below that must be true. O A. Span(y, w) = Span(z) О в. Span(y) %3D Span(w) C. Span(x, y) = Span(w) О D. Span(x, у) - Span(x, w, z)

Q: If a vector u is orthogonal to vectorsx and y then u is orthogonal to the vector x + y.

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Q: Let u and v be two non-zero vectors in R". Which of the following options can we conclude are equal…

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Q: Suppose v, w, z are vectors in R". Show that if r and y are linear combinatio: v, w, and z, then r+…

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Q: 6. If u,v, and w are three vectors in R', describe their linear span.

A: 6. If u,v and w are three vectors in R7, we have to describe linear span.

Q: Please help me number 6. Thanks!

A: We are given that the unit vectors x, y, z satisfies the equationTo find the relation between the…

Q: Find the vector component of u = ⟨5, 10⟩ that is orthogonal to v = ⟨4, 3⟩, given that…

A: Given,      w1 = projvu = ⟨8, 6⟩   and     u = ⟨5, 10⟩ = w1 + w2.      Where,  u = ⟨5, 10⟩ ,  v =…

Q: Let w, x, y, z be vectors and suppose z = 4x + y and w = 16x + 5y – 4z. Mark the statements below…

A: Given z=4x+yw=16x+5y-4z

Q: Let x, y, z be (non-zero) vectors and suppose that z = -3x+ 4y and w = -6x + 8y – 4z. Are the…

A: Solution for 1: Given that  x, y, z be (non-zero) vectors such that z=-3x+4y and w=-6x+8y-4z. Now,…

Q: Let x, y, z be (non-zero) vectors and suppose w = 12y – 9x + 2z. If z = 3x – 4y, then w = x+ 4 y.…

A: Vector spinning sets

Q: Let w, x, y, z be vectors and suppose z = 4x + y and w = 16x + 5y – 4z. Mark the statements below…

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Q: a) If possible, express w as a linear combination of vectors u and v. w = - (1,0, —7), и %3D…

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Q: If a vector u is orthogonal to vectors x and y then u is orthogonal to the vector C1X – C2y. Select…

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Q: a) If possible, express w as a linear combination of vectors u and v. w = (1,0, –7), u = (1,3,4), v…

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Q: u.v<0, u.w < 0 ,w .u < 0 ?

A: Given data:     The given first vector is: u. The given second vector is: v. The given third vector…

Q: Can three vectors in the xy plane, R^2, have u.v<0, v.w<0, w.u<0

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Q: · Let 2 be the separation vector from a fixed point (x', y', z') to the point (x, y, z), and let z…

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Q: Consider two vectors A and B prove that the cross product between them can be calculated as follows…

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Q: Verify that the two planes are parallel. -x + 6y + 2z = 8 -x + 3y + z = 9 2. Find the normal vector,…

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Q: Let v be a vector of length 2. If w = -5v, u = (-2, –2) and the angle between w and u is . then v x…

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Q: Let y = and u = Let L be the line spanned by u. Write y as the sum of two orthogonal vectors, YL in…

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Q: Let x,y,z be (non-zero) vectors and suppose that z=4x−4y and w=12x−12y−4z. Are the following…

A: A vector is a span of vectors when the first one can be written as the linear combination of the…

Q: Let æ, y, z be (non-zero) vectors and suppose w = 12y – 9x + 2z. If z = 3x – 4y, then w = -3 x+ 4 y.…

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Q: Let w, x, y, z be vectors and suppose z = 4x + y and w = 16x + 5y – 4z. | Mark the statements below…

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Q: Let x, y, z be (non-zero) vectors and suppose w = 4y – 3x – 2z. If z = 4y – 3x, then w = x+ y. Using…

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Q: Verify the Pythagorean Theorem for the vectors u and v.u = (4, 1, −5), v = (2, −3, 1)

A: Given   The vector u = (4, 1, −5), v = (2, −3, 1) Pythagorean Theorem for the vectors

Q: Let w,x,y,z be vectors and suppose z=−4x−3yand w=−16x+4y−4z Mark the statements below that must be…

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Q: Suppose f(x,y)=4x2+y^2 and u is the unit vector in the direction of ⟨2,1⟩. Then, (a) ∇f(x,y)=  (b)…

A: We have  f(x,y)=4x2 +y2

Q: Use the fact that the volume of a tetrahedron with adjacent edges giver by the vectors u, v and w is…

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Q: Let a, y, z be (non-zero) vectors and suppose w = 4y – 16x + 3z. If z = 4x – y, then w x+ y. Using…

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Q: Let w, x, y, z be vectors and suppose z = 4x + y and w = 16x + 5y – 4z. | Mark the statements below…

A: We have to use the equations z=4x+y and w=16x+5y-4z to describe the relationship between the vectors…

Q: Let x, y, z be (non-zero) vectors and suppose w = 12y – 9x + 22 If z = 3x – 4y, then w = -3 x+ 4 Y.…

A: Given that w=12y−9x+2z z=3x−4y

Q: Suppose we know that u · v = u · w. Does it follow that v = w? If it does, give a proof that is…

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Q: Find a vector x = ( c, d) that has dot products x · r = 1 and x · s = 0 with two given vectors r =…

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Q: Let w, x, y, z be vectors and suppose z = -2x – y and w = 2x + 3y + z. Mark the statements below…

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Q: Let x, y, z be (non-zero) vectors and suppose w = 12x + 6y + 4z. If z = -2x - y, then w = 4 ✔B.…

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Q: Suppose a vector y is orthogonal to vectors u and v. Show that y is orthogonal to the vector u + v.…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Consider the vectors u =(4,2,-11), v=(5,0,-9) and w =(x,y,11). For the vector w'to be orthogonal to…

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Q: = Span(y, w) Span(w)

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Q: Suppose that u and v are two unit vectors in 3D and the angle between them 6 i. What is |u x v[? ii.…

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Q: Let y→=[−8, −7] and u→=[−2, 6]. Write y→ as the sum of two orthogonal vectors, x→1 in Span{u} and…

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Q: For the vector PP, , its norm satisfies PP, =2. The inscribed angles between PP, 2 2 and x-axis and…

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Q: Let x, y, z be (non-zero) vectors and suppose w = 12y – 9x + 2z. If z = 3x – 4y, then w =-3x + 4y |…

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Q: Linear algebra

A: From the given information:Let,

Q: Let y = 185 || 3 and u = Write y as the sum of two orthogonal vectors, ₁ in Span {u} and 2…

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Q: Let x, y, z be (non-zero) vectors and suppose w = 5x – 15y – 3z. If z = x – 3y, then w = 2 x+ -6 y.…

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Q: Suppose that u, v. and w are vectors such that (u, v) = 2, Evaluate the given expression. (v, w) = -…

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Q: What is the dependence on the following vectors: u=(3.0.1), v=(1,-1,0) and w=(1.0.1) thanks!

A: A set of vectors {v1,v2,...,vn} in Rn is said to be linearlyindependent if the vector equationx1v1 +…

Q: et x = [7, -4, -8] and y = [-6, -6, –10] be vectors in R'. Compute the following: %3D a+y [ -8x = […

A: Let's find.

Q: For what values of y are the vectors yi – 2j + 3y k and 6i +j+ 3y k orthogonal.

A: To find the values of y for which the vectors yi-2j+3y k and 6i+j+3y k are orthogonal.