Gve an example of a dx2 matrix A and 2-dimensional vectors u and v such that u and v are orthogonal to each other but the vectors Au and Av are not or thogonal to each other.

Q: Find the coordinate matrix of x in R" relative to the basis B'. B' = {(6, 0), (0, 2)}, x = (48, 10)

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Q: Complete the matrix A so that it is skew-Hermitian. i 2—6і - A = 1 9i Y = = 2

A: Given the matrix, A=0i2-6ix01yz9i The matrix A is said to be skew-Hermitian matrix if, A*=-A Where…

Q: Determine whether the matrix is orthogonal. An invertible square matrix A is orthogonal when A−1 =…

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Q: Find the coordinate matrix of x in R^ relative to the basis B'. B' = {(5, 0), (0, 2)}, x = (10, 8)…

A: If A is a basis, then x∈Rn can be written as linear combination of the elements of A. When a scalar…

Q: Let U = {u1, u2} and W = {w1, W2} be bases for V, and let P be a matrix whose columns are u1 w and…

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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 coordinate matrix of x in R'" relative to the basis B'. B' = {(9, 0), (0, 7)}, x = (27, 28)

A: We have given basis B' and x, and we have to find corresponding coordinate matrix [x]B'.

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

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Q: Let {v1, v2, ..., vn} be an orthogonal set in R" with respect to the Euclidean inner product. Let A…

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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: Let A denote the 2 x 2 matrix We define a function (, ) : R² ×x R² → R by taking (x, y) = y" Ax, for…

A: We have A=1221. We are given the function ·, · : ℝ2×ℝ2→ℝ by taking x, y=yTAx, for each pair of x,…

Q: Prove Theorem

A: (a)   Let A=a11a12...a1na21a22...a2n⋮⋮⋱⋮am1am2...amn…

Q: 5. Give 2 x 2 matrices A so that for any x e R² we have, respectively, (f) Axis the vector obtained…

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Q: Taking each column of the matrix as a vector, the linear combinations of these column vectors form a…

A: Write RREF form for given matrix then basis is the original columns corresponding pivots.

Q: Let A be an m×n matrix. Explain why the followingare true. Any vector b ∈ Rm can be uniquely written…

A: For  matrix A, N(A) is the null space of A. R(A) is the column space of the matrix A and R(AT) is…

Q: Find the coordinate matrix of x in Rn relative to the basis B′.B′ = {(1, 2, 3), (1, 2, 0), (0, −6,…

A: Given

Q: Need help finding the Jordan Canonical Form, an invertible matrix P such that J=P^-1MP And J^9

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Q: Determine whether the matrix is orthogonal. An invertible square matrix A is orthogonal when A-1 =…

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Q: Determine whether the matrix is orthogonal. An invertible square matrix A is orthogonal when A-1 =…

A: To Know if a Matrix is Orthogonal: To check if a given matrix is orthogonal, first find the…

Q: Determine whether the matrix is orthogonal. An invertible square matrix A is orthogonal when A−1 =…

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Q: (a) Let A, B be n × n symmetric matrices such that XTAX = X™BX for all column vectors X e R". Show…

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Q: Let A be an m×n matrix. Explain why the followingare true. Any vector x in Rn can be uniquely…

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Q: (c) Show that a normal 2 x 2 real matrix is either hermitian, skew- hermitian or a constant multiple…

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Q: Determine whether the vector u belongs to the null space of the matrix A. Solve it on scratch. 1.

A: Here u belongs to Null(A) if and only if Au=0.

Q: ) Consider the quadratic form Q(x) = x" Ax, where A = 2 2 2 0 2 %3D Write out Q(x) in terms of z1,…

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Q: A real square matrix Q is called orthogonal if QTQ = I. Prove det(Q) = ±1. Give an example of such a…

A: Solution

Q: a) Consider the NxN-dimensional invertible matrix A and the N-dimensional (column) vector u. Prove…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Diagonalize the quadratic forms by finding an orthogonal matrix Q such that th e change of variable…

A: Given: The quadratic form is given as  f(x, y) = x2 + 8xy + y2

Q: Find the coordinate matrix of x in R" relative to the standard basis. х%3D (2, —3, —4, 9) [x]s = %3D

A: Here x is a vector in R4

Q: Determine if the vector u is in the column space of matrix A and whether it is in the null space of…

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Q: Determine whether the matrix is orthogonal. An invertible square matrix A is orthogonal when A−1 =…

A: Now transpose of this matrix is,

Q: Find the coordinate matrix of x in R" relative to the basis B'. B' = {(4, 3, 3), (-11, 0, 11), (0,…

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Q: Matrix A=(a)nxn is called strictly diagonally dominant, if "1 |a₁|> Σ |aj|, Σ |aj|, i=1,2,...,n.…

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Q: 5. Let x and y be vectors in R" and let Q be an n x n orthogonal matrix. Show that if z = Qx and w =…

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Q: Find the coordinate matrix of x in RM relative to the basis B'. B' = {(8, 11, 0), (7, 0, 10), (1, 4,…

A: Given that, B'=8, 11, 0, 7, 0, 10, 1, 4, 6 and x=5, 34, -2

Q: Determine whether the matrix is orthogonal. An invertible square matrix A is orthogonal when A−1 =…

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Q: Find the coordinate matrix of x in R" relative to the basis B'. B' = {(4, 3, 3), (-11, 0, 11), (0,…

A: The given vector space is  with basis B'=4,3,3, -11,0,11, 0,9,2. Consider the vector x=26,3,-19∈R3.…

Q: Find the coordinate matrix of x in R" relative to the basis B'. B' = {(8, 0), (0, 9)), x = (16, 54)…

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Q: (a) Find the matrix representation of L(x), the linear operator on R? that first rotates by 30°…

A: Vectors.

Q: Give an example of a matrix A and a vector b such that the solution set of Ax = b is a line in R'…

A: System of linear equations

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

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Q: Find the coordinate matrix of x in R" relative to the basis B'. B' = {(4, 3, 3), (-11, 0, 11), (0,…

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Q: Let A and B be square matrices of order 2 such thatA=-7 and B=4.What is (ABY"| %3D %3D

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Q: b. Let B = {T1, đ2, 73}, C = {71, 72, T3}, %3D be two orthogonal bases for R³. Show that the…

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Q: Let A be nxn orthogonal matrix and v E R". Then ||Av||? = || ||?. %3D Select one: True O False

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Q: Complete the matrix A so that it is Hermitian. 1 i 7 – 3i A = -3 1 4 Y = Z =

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Q: Find the coordinate matrix of x in R relative to the basis B'. B' = {(8, 11, 0), (7, 0, 10), (1, 4,…

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Q: Find the coordinate matrix of x in R^ relative to the basis B'. B' = {(5, 0), (0, 7)}, x = (40, 21)…

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Q: Let A be a 2x2 matrix, c a scalar. Then det(cA)= c*det(A). Select one: O True False

A: Select one: True or false:

Q: Find the coordinate matrix of x in R" relative to the basis B'. B' = {(5, 0), (0, 9)}, x = (40, 45)…

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