2. Use matrix multiplication to find the orthogonal projection of (1, 2, - 3) onto the a. ху-plane. b. xz-plane.

Q: 5. Show that if each of the vectors {Bo, B1,...,B,} is a linear combination of {a1,a2,...,a,}, then…

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Q: 7. Use matrices to stretch the vector horizontally by a factor of 3.

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Q: Compute the orthogonal projection of 7 = projz (7) = onto the line L through and the origin.

A: The given data is: v→=-69 To compute the orthogonal projection of v→=-69 onto the line L through -76…

Q: and = %3D are oignualus of a matrix A Corraspondeng to the egnualuong=2 and >=-2 then = ACTa t Ja)=…

A: For a given matrix A if 'x' is eigen vector of matrix A corresponding to the eigen value ' q ' then…

Q: Compute the orthogonal  projection of v = [ -3, -3 ] onto the line L through [ 2, -2 ] and the…

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Q: Compute the product 0 () 0 (²) as a 2 x 2 matrix. What kind of isometry is this product?

A: Given product is  Oπ5O2π15 where Oθ represents rotation matrix through an angle θ in anti-clockwise…

Q: Find the standard matrix for the reflection T of R³ on the line , = . Your work must be shown! Is T…

A: We will first take an arbitrary point (x,y,z) then calculate its reflection point (x',y',z') about…

Q: Verify the orthogonality p

A: answer is in next step

Q: For a C4 axis along z axis, please find the matrix for c, the synmetry opertion on a vector·

A: Given, C4 axis is along z axis . Upon action of C14 symmetry operation, the change with respect to x…

Q: A vector is rotated about the Y-axis 45 degrees and is subsequently rotated about the fixed X-axis…

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Q: Find the projection of ū = (2, -3, 1) onto v = = (-3, 0, 1) %3D 3 0, А. B. (3.0. -1) В.

A: u→ =2, -3, 1v→ =-3, 0, 1v→ =(-3)2+02 +12       =9+1|v→| =10    u→  · v→ =2, -3, 1·-3, 0, 1u→  · v→ =…

Q: Let a = (2,3,6) and b = (3,4,2) be vectors.  Compute the cross product aXb

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Q: Show that the three points (x1, y1), (x2, y2), and (x3, y3) in a plane are collinear if and only if…

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Q: Let Q be an orthogonal 2 X 2 matrix and let x and y be vectors in R2. If θ is the angle between x…

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Q: Find the vector projection of (3, 3, 4) onto (–1, -2, 2).

A: Projection of u onto v is given by.

Q: What scaling matrix S (in homogeneous coordinates, so 3 by 3) would produce a 1 by 1 square page…

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Q: 8. Determine the dot product of u = [5,-3,1] and v=| 1v=[2,-2,3].

A: Please see the below answer.

Q: Find the standard matrix of the linear operator M : R → R³ that first rotates all vectors…

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Q: , counting the multiplicities. Then A is orthogonally diagonalizable.

A: We have to examine that matrix A is orthogonally diagonalizable or not.

Q: Find the matrix of the orthogonal projection of R² onto ar + by 0. %3D

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Q: 3) Let B, = {u,, u2} and B2 = {v,, v3} be the bases for R° in which u, = (1,2), uz= (2, 3), v =…

A: The solution is given as

Q: Calculate the projection matrix of R3 onto the line spanned by (5, 1, −3)

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Q: orthonormal 3D vectors

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Q: Find the standard matrix for the linear operator T: R^3 --> R^3 that first rotates a vector…

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Q: Find the matrix of the reflection about the line L.

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Q: Find the matrix A representing the reflection about the line L in R² which consists of all scalar…

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Q: Find orthogonal projection of u=(-1, 2, 5) in the direction of v=(3, 1, -2).

A: find the orthogonal projection of u=-1,2,5 in the direction of vector v=3,1,2 it is known that…

Q: Given the vector u = (4, 1, -6) and a = (1, O, 5). The orthogonal projection of u on a (projau ) is…

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Q: suppose A be any Hew of have symmetric matoir order and this matrix 4x4 rank of 3 the caleulata the…

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Q: Given Pauli matrices X,Y, Z ; show that X2 = Y2 = Z² = 1 (a) by using the matrix representation (b)…

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Q: If Pis the projection matrix onto the line through (C) (:) and then I - P projects onto the line…

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Q: 2 then the is the matrix of transition from the base B to the basis B' and the coordinates of vector…

A: Given that B and B' are bases of a vector space v and P is the matrix of transition from base B to…

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: Find a basis for R3 that includes the vectors (1, 0, 2) and (0, 1, 1).

A: Given vectors 1,0,2 , 0,1,1IR3 is a vector space of dimension 3 Let , the standard basis for IR3is…

Q: Suppose A is rectangular ( m by n) and S is symmetric ( m by m).(a) Transpose AT SA to show its…

A: Given: Matrix A is rectangular ( m by n) and matrix S is symmetric ( m by m).

Q: Compute the standard matrix for the linear map T : R² → R² which (1) rotates i by 0 = T, (2)…

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Q: Suppose A and B are both orthogonally diagonalizable and AB = BA. Explain why AB is also…

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Q: 4 2. Decide whether the vectors (1, 2,0,-1], [2, 6, -3, -3], [3, 10, -6,-5] are linearly…

A: Given vectors are ,  [ 1,2,0,-1 ] ,  [ 2,6,-3,-3 ] ,  [ 3 ,10 ,-6 ,-5 ]  (.)  The given vectors are…

Q: Compute the standard matrix of the linear operator M : R³ → R° that first reflects all vectors about…

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Q: If P is the projection matrix onto the line through () -- (;) C) and ) then I – P projects onto the…

A: I have checked one by one option wise

Q: Use Gram-Schmidt to find an orthogonal basis for R if B={(-5, 2), (3, -1)}.

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Q: Find Vector production of b onto a  a=(-3,4) b =(6,7)

A: Given data: The first vector is a=(-3, 4). The second vector is b=(6, 7). The dot product of b and a…

Q: Suppose A is invertible and orthogonally diagonalizable. Explain why A–1 is also orthogonally…

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Q: Find orthogonal projection of v=(3, 1, -2) in the direction of u=(-1, 2, 5).

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Q: Find the matrix P that multiplies (x, y, z) to give (y, z, x). Find the matrix Q that multiplies (y,…

A: The matrix “P” will be, P=010001100  if multiplies (x,y,z) to give (y,z,x) Explanation:…

Q: Find the matrix A of the rotation about the z-axis through an angle of clockwise as viewed 2. from…

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Q: Suppose that u, and uz are orthogonal vectors, with ||u1|| = 5 and ||u2|| = 2. Find ||4u1 - u2||- ||…

A: Let,        u=x1i+y1j+z1kand v=x2i+y2j+z2k It is given…

Q: Determine the orthogonality of ψ111 and ψ121 for a three-dimensional particle in a box.

A: Needed formula: ∫sin2axdx=x2-14asin2ax+Ccos A+B-cosA-B=2 sin A sin Bsin nπ=0, n=1,2,...

Q: Find the standard matrix for the stated composition of linear operators on, orthogonal projection on…

A: Reflection Matrix about the xy-plane is : Rxy=10001000-1 Reflection Matrix about the xz-plane is :…

Q: Prove that swapping the order of vectors in the cross product changes the sign of the output: ьха3 -…

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