6ij=I, V i,j from 1 to 3 where I is identity tensor matrix.

Q: Find the coordinate matrix of w relative to the orthonormal basis B in Rn.

A: Let,

Q: Find the stable vector of 1 1 1 P = 2 1 3 3

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Q: Let x and y be linearly independent vectors in Rnand let S = Span(x, y).We can use x and y to…

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Q: Let Q be an m x n matrix with columns forming an orthonormal set. Show that (Qx) · (Qy) = x · y for…

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Q: Determine all values of the parameters x and y such that the vector 1 s in the range of the above…

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Q: uèstion 2 If u1, u2, U3 are 3 orthonormal vectors of R, then the 3x3 matrix A =[u, u,u3]is…

A: This type matrices are always an orthogonal matrix.  And inverse will be the transpose

Q: Find the inverge of the 2x2 matrix Cos t Sin t - Sine Cose

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Q: Answer considering the matrix with the given vectors as its columns

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Q: Let x and y be vectors in Rn and let Q be an n × n orthogonal matrix. Show that if z = Qx and w = Qy…

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Q: (a) Using Gaussian elimination, find a vector v such that

A: As per our guideline is multiple questions are posted we are supposed to answer only the first one.…

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: Let u = [-1 3 -1] and v =[-6 0 5]. Find the vector w = 2u – 7v and its additive inverse. %3D

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Q: Let u=(-1,37 and u =< 2,-57 Find the Component form of the vector Su-V

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Q: Answer considering the matrix with th e given vectors as its columns

A: Given: The given matrices are, Assume the linear combination as follows,

Q: 21 Find the matrix that projects a vector from R onto the column space of the matrix 0 12 4

A: Consider the matrix A=120124. Columns of A are 102 and 214 . Clearly, they are linearly independent.

Q: Obtain a vector orthonormal to the vectors i−j  and (1, 0, 1)

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Q: Find the stable vector of 1 2 1 3 2 3

A: ANSWER:

Q: Find the stable vector of 1 3 4 4 P = 4 %3D 3 7

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Q: Let x = 8i – 5j - and y = 3j – 7k be two vectors. Find the value of the scalar product x · y.

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Q: Show that if annxn matrix U satisfies (Ux)· (Uy) = x•y for all x and y in Rn, then U is an…

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Q: What is the determinant formula for calculating the cross product of two vectors relative to the…

A: Consider two vectors relative to the Cartesian i, j, k-coordinate system.

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

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Q: 1) Express this is in vector form / matrix form

A: A matrix is an array of numbers, a multi-dimensional, whereas a vector is a one-dimensional list of…

Q: Find the stable vector of 0 0 1 1 P 2 1 3 3 ..-

A: It is an important part of statistics. It is widely used.

Q: Let MS be the n × n matrix whose j th column is v j and let MT be the n × n matrix whose j th column…

A: Given: Here it is given an n×n matrix of Ms whose jth row is Vj as well as an n×n matrix MT whose…

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: Define what it means for a function Q : R" R to be a quadratic form. Furthermore, explain how we…

A: The quadratic form is one of the most important parts of linear algebra. Quadratic means degree two.…

Q: Find a vector orthogonal to (0, 1, 7) and (2i – j+ 4k) 11i + 14j - 2k 2i - j+ 11k -j + 28k 4i + 14j…

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Q: Find the scalar and vector projections of b onto a, where a = (-1,1,2) and b = (-4,5,8).

A: The solution of the problem is given in the next step.

Q: (a) Let M be a square matrix such that M² = 0. Let t, c be scalars and c‡0. Show that

A: We shall solve first question only as you have asked more than one different question - for others…

Q: Give the General Solution:  (d/dt)(vector(x)) = matrix(-2,1,0,-2)vector(x)

A: The given system is as follows. ddtX=-210-2X Find the eigenvalues of the coefficient matrix as…

Q: -) Let A, B be nx n symmetric matrices such that XTAX = X™BX for all %3D column vectors X e R". Show…

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: Let aj be a nonzero column vector of an m×n matrix A. Is it possible for aj to be in N(AT )?…

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Q: ers such that p2 e matrix

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Q: Find the scalar AND vector projections of a onto b where a=(0,1,-2) and b=(-1,0,3)

A: Given , a = (0,1,-2) and b = (-1,0,3).

Q: Find the volume of the parellepiped spanned by the three given vectors à, v and w (hint: use a…

A: The volume will be u.(v×w), the cross product will br applied be the determinant.

Q: Use matrices to transform the vector .3 by a reflection across the x-axis, a horizontal compression…

A: Given:     Vector : ⟨ 7 , 3 ⟩     Reflection across x - axis   Horizontal compression = 1/2…

Q: Find the stable vector of 1 2 4

A: The stable vector is the probability row vector w such that w*P=w Let , w= [ x  y  z ] So it becomes…

Q: Find the coordinate matrix of x = (-17, 22) in R² relative to basis B' = {(-5,6), (3, –2)}. %3D %3D

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Q: If A is second order tensor ,then ylgn O ihi O

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: +0, then the matrix H = I – 2- vv7 is orthogonal and symmetric. Show that if the vector v

A: Given  H=I-2vvTvTv

Q: Q3, Write any matrices A and B of order 3 x 3 and verify the results Let A and B be n x n matrices,…

A: Write any matrices 'A' and 'B' of order 13×3 A=110012003    B=013100100 To verify 1)…

Q: Let TA : R → R³ be multiplication by the orthogonal matrix 1 21 3 3 3 6- 1 Find TA(x) for the vector…

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Q: Determine which set of vectors form an orthonormal. a) b) c) d) None of these 11L

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Q: 8) Let A be an nxn ma tiX. vector b the equation Ax = b has more than one solution. Explain why A is…

A: Invertible matrices

Q: Gve an example of a dx2 matrix A and 2-dimensional vectors u and v such that u and v are orthogonal…

A: We have to give an example of a 2×2 matrix.

Q: Find the vector, not with determinants, but by using propertles of cross products. (1 x ]) x k Watch…

A: Cross products property i x j = k           eq(1) j x k= i k x i= j And i x i=0 , j x j=0 and k x…

Q: 4) Show that, in general, (A.B)" = B".AT How is (A.B) related to (B.A) when both tensors A and B are…

A: 4.

Q: A=30 ,B = Find the 3x3 homogeneous matrix for 2D-reflection across a line that goes through (B, C)…

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Q: Complete the matrix A so that it is Hermitian. 6 – 3i 1 A = -4 1 2 2 =

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.