Show that except in degenerate cases, (u * v) * w lies in the plane of u and v, whereas u * (v * w) lies in the plane of v and w. What are the degenerate cases?

Q: Let V = R2, defined the addition by: (uz +u2) + (vị + vz)= (U1 +V1 , Uz +V2 + 1) With standard…

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Q: find the projection of v onto u.

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Q: (a) Prove that u + vand u - v are orthogonal in IR" if and only if ||u|| = ||v||. (b) Draw a diagram…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: If x, y and z are vectors in an inner product space such that (x, y) = (x, z), then y = 2.

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: Show that, in an inner product space, there cannot be unit vectors u and v with <u, v > <…

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Q: Show that (x, y) = 5x1y1 – 9x2y2 for vectors x = (x1, x2) and y = (y1, y2) in R2 defines an inner…

A: This question is about application of linear algebra

Q: Recall that R, denotes the Sorgenfrey line. Express the basis for the topology on R,?.

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Q: Prove that u is orthogonal to v - proju(v) for all vectors u and v in Rn, where u ≠ 0.

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Q: Let V = {(x, y): x 20) with standard operation on R2. Is V a vector space?

A: Given set is  V={(x,y):x=>0 }

Q: Let y = and u = Write y as the sum of two orthogonal vectors, y, in the span of u, and y, which is…

A: Solution

Q: Let ā = (1,2),b = (x,y) and = (1,-2) find the value of x and y such that a is %3D %3D %3D orthogonal…

A: Given that a is orthogonal to b So a·b=0also we have c·b=2

Q: Let r = (2,-i, 1), and y = (-i, 3,1 + i) be vectors in C3. Compute (x, y), ||x||, |ly|l, and…

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Q: _3. Let x be a convex combination of {y1, . . , yk }. Assume in turn that each y; is a convex…

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Q: Also deduce the Jacobi identity for the cross product: u × (v × w) +w × (u × v) +v × (w x u) = 0 их

A: Introduction: We know that u×v×w=vu·w-wu·v, where u, v, and w are purely imaginary.

Q: Let (V, (, )) be an inner product space and let v, w be vectors in V. If (v, w) = 7 and w = 5, then…

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Q: 2. Follow the directions of Exercise 1 using the weighted Euclidean inner product (u, v) = }u,V, +…

A: As per the company guidelines we are supposed to answer only first three subparts.Kindly repost the…

Q: Let V ((x,y): x 20) with standard operation on R2. Is V a vector space?

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Q: Find vector x and y in R? that are orthonormal with respect to the inner product (u, v) = 4u1v1…

A: Let x=14,0, y= 12,0 Hence, by using the given inner product, we have x,y=414(0)…

Q: Find the projection of u onto v.

A: Given,            u= < 2, 1, 3 > and  v= < 1, 0, -4 > and w = < 1, 1, 5 >

Q: Show that 4(u, v) = ||u+v||² – ||u – v||2 for all u, v in an inner product space V (V - -

A: Given: The given equation is, 4u,v = u+v2-u-v2 Here we know, real vector space is V so that u,v is…

Q: State why (u, v) is not an inner product for u = (ui, u:) and v = (v, V2) in R? %3D (u, v) = (u,v;)²…

A: We are given that u,v=u1v12+u2v22 for u=u1,u2 and v=v1,v2 in R2. We know that an inner product must…

Q: Show that V={(x,2020x): x in R} is a vector space

A: According to the given information, it is required to show that the given set is a vector space.

Q: find the projection of v onto u.

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Q: Let V = {(x, y): x 20} with standard operation on R². Is V a vector %3D space?

A: Our objective is to conclude V is a vector space or not.

Q: Show that every plane through the origin in R3 may be identified with the null space of a vector in…

A: The null space of any matrix A consists of all the vectors B such that AB = 0 and B is not zero.It…

Q: find the projection of u along v  u = (1, 1, 1), v = (1, 1, 0)

A: the given vectors are: u=1,1,1v=1,1,0 we have to find the projection of u along v.

Q: Let V = {(x, y): x 20} with standard operation on R2. Is V a vector space?

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Q: Find x such that the vectors xi+2j -3k, i+j ,j+3k are Coplanars (lies the Same Plane) . on

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Q: Let V = {(x,y) where y= 3x+1 x ER} with scalar multiplication defined by k(x,y)=(kx,y) is a vector…

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Q: If ã = <!,2,37 and b=<5,0 -17, find the vector pojection of %3D %3D ŏ onto à.

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Q: 10. Show that V = R² with the standard scalar multiplication, but addition defined by (7, , v.) +…

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Q: If x, y are two no vectors, then prove that |xty | || X lle y llq by = + // use Holder inequality.

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Q: Compute the orthogonal projection of i = |0| onto W = Span 3

A: Here, u→=103v1→=012v2→=410

Q: Consider R' endowed with the dot product. Let W = span{u1, u2} where u1 = (1,0, 1) and u2 = (-1, 1,…

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Q: Find the projection of u onto v, proj,u, given u = and v = .

A: PFA

Q: Calculate the cross product assuming that u x w иxw3D (2, 6, 1)

A: Given vector u x w &lt;2, 6, 1&gt;

Q: Let II be a plane passing through the origin, and let n be a non-zero vector orthogonal to II. Then…

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Q: If u = (3, −1, 4) and v = (−2, 3, 5), the scalar projection of y onto v is:

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Q: 2. Show that the ry plane W = (r, y, 0) in R³ is generated by: (i)u = |2 and v= (ii)u = and v=

A: Please see the below picture for detailed solution.

Q: Find all vectors in R2 that are orthogonal to u = (2,1).

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Q: Let (V, (, )) be an inner product space and let v, W be vectors in V. If (v, w) : = 7 and |w| = 5,…

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Q: Find a linear mapping G that maps [0, 1] x [0, 1] to the parallelogram in the xy-plane spanned by…

A: Given: The maps [0, 1] x [0, 1] to the parallelogram in the XY-plane spanned by the vectors (2, 3)…

Q: ind the norm of x and the unit vector u in the direction of a if -5 * = ||| = %3D 2 2

A: The norm of a vector A→=abc is defined by A→=a2+b2+c2.

Q: SHOW THAT THE SET OF POLYNOMIUMS HAS A VECTOR SPACE OF POLYNOMIALS OF A LESS DEGREE THAN “g”  (Pg…

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Q: Let x, y, and z be vectors in Cn and let α and β becomplex scalars. Show thatz, αx + βy} = α z, x} +…

A: Given: z,αx+βy=αz,x+βz,y

Q: Show that (x, y) = 4x1y1-7x2Y2 for vectors x = (x1, x2) and y = (V1 Y2) in R2 defines an inner…

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Q: SHOW THAT THE SET OF POLYNOMIUMS HAS A VECTOR SPACE OF POLYNOMIALS OF A LESS DEGREE THAN “g”  (Pg…

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