Let T, be any general n by n tridiagonal matrix. What is the total of the number of multiplications and divisions needed to determine the LU-decomposition of T„ ? ( Note that there is no right-hand side vector f .)

Q: Construct a 3 x 3 triangular matrix A so that 1] the vector 2 is in Col A. 3]

A: We know every lower or upper traingular matrix is a triangular matrix.

Q: and Find the matrix A of the orthogonal projection onto W. A =

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Q: Let Q be an orthogonal matrix such that QA makes sense. Show that A and QA have the same singular…

A: Let,

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A: Let,

Q: Find the matrix A of the orthogonal projection onto the line L in R² that consists of all scalar…

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Q: (AB)† = B†A† (AB)−1 = B−1A−1

A: This is a question of linear algebra. The first one is important property regarding conjugate…

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 coordinate matrix of x relative to the orthonormal basis B in R". . {(금 승, 이 (-승릉이 0.0, 1}…

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Q: 3. In the of square matrix M2x2 find representation of vector A = from the L4 space basis U2 %3D ;…

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Q: The set of all real two-dimensional row matrices {la b]} with standard matrix addition but scalar…

A: We identify the property that 1.x=x

Q: Let A Mn(C) be a Hermitian matrix. &

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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: Compute the product M (0)0 (7) as a 2 x 2 matrix. What kind of isometry is this product?

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Q: 5. Give an example of a matrix A such that im(A) is in R2 is spanned by the vector A = %3D

A: Given that, A is a matrix such that imA is in ℝ2 is spanned by the vector 52

Q: Suppose that an nxn matrix A has a QR-decomposition where

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Q: Assume that we obtained the column vectors of 0 11/2 by applying the Gram-Schmidt process to the…

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: Is it true or false? If A is nxn matrix, c is scalar, then cA |=c | A| Birini seçin:

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Q: Let U be the vector space of 3×2 matrices over R. Show that dim.U =6.

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Q: Prove that an m X n matrix A has rank 1 if and only if A can be written as the outer product uvT of…

A: Given that an m X n matrix A has rank 1 if and only if A can be written as the outer product uvT of…

Q: Find the matrix of the standard inner product on W (obtained by restriction of the dot product on…

A: “Since you have asked multiple questions, we will solve the first question specified by you i.e.…

Q: Suppose that x and y are mxn matrices. Prove that xT- yT=(X -YT. Find a 2x2matrix A, that is not the…

A: Take A and B as arbitrary m×n matrices and evaluate the left and right sided expression

Q: Find the coordinate matrix of x in Rn relative to the standard basis.x = (1, −3, 0)

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Q: Prove If U is a unit upper triangular matrix, then U is nonsingular and U−1 is also unit upper…

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Q: In the vector space P of polynomials of degree at most two, the second column of the matrix of…

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Q: Find the standard matrix of the compositetransformation from R2 to R2.     Counterclockwise rotation…

A: Let T : R2→R2 be the counterclockwise rotation through 60° about the origin and let S : R2→R2 be the…

Q: (a) If A e Mmxn(F) and A UEV is its singular value decomposition, explain how we obtain the entries…

A: a) if A∈Mm×nF and A=U∑V* is  its singular value decomposition, explain how we obtain the entries of…

Q: Now assume that f and g are both C2. Express the matrix of second derivatives V²F(x) in terms of f…

A: b)

Q: Prove that if a square complex matrix is unitarily diagonalizable, then it must be normal.

A: Every square complex unitarily diagonalizable matrix is normal. Let, A be a square complex unitarily…

Q: Prove the Frobenius theorem in the case where A is a 2 ×2 matrix.

A: This theorem is not valid for order less than 3

Q: Let A be an Hermitian matrix and let B = iA. Show that B is skew Hermitian.

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Q: If A is an m × n matrix of rank r, what are the dimensions of N(A) and N(AT )? Explain.

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Q: Prove det(A) = det(A'), for an upper triangular matrix A.

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Q: Find the coordinate matrix of x relative to the orthonormal basis B in R". {G ) (-) 0, 0, 1)} x =…

A: Given vector is x=20, 10, 25 and the corresponding orthogonal basis is B=35, 45, 0, -45, 35, 0, (0,…

Q: Let A = CD, where C and D are n × n matrices and C is invertible. Prove that the matrix product DC…

A: A = CD, where C and D are n × n matrices, and C is invertible. We need to Prove that the matrix…

Q: Let A € RPXm have rank r. Show that there are matrices C and B such that A = св, where C E RPXT and…

A: Please check the solution in next step

Q: Let A = UEVT be a SVD of a square matrix A. What is the product of the diagonal elements of E, in…

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Q: Find an explicit description of the null space of matrix A by listing vectors that span the null…

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Q: Let A E Mn(C) denote the n x n matrix with all entries equal to 1. Show that A is positive…

A: Let A belongs to  Mn (C) denote the n x n matrix with all entries equal to 1. Show that A is…

Q: Let W be the vector space of 3x3 symmetric matrices, A E W. Then, which of the following is true? a)…

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Q: Let A be an m x n matrix, let P be the projection matrix that projects vectors in Rm onto R(A), and…

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Q: Let A be an n x n matrix. Then A is nonsingular if and only if its column vectors form a basis for…

A: We have to check

Q: Find the coordinate matrix of x relative to the orthonormal basis B in R". {(금, 승 이) (-승름이 (0,0, 1}…

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Q: Find the coordinate matrix of x relative to the orthonormal basis B in R". {( 3/10 0, 10 V10 3/10 0,…

A: The solution is given as

Q: Let A be a 4x4 singular matrix. What is the smallest possible dimension of Null Space of A? A) 2

A: Using,  Rank- Nullity Thereom

Q: Let A be an 2 x 3 matrix and b be a vector in R" such that the system Ax = b has solution set 0. 0.…

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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: Find a formula for the dimension of the vector space of symmetric n X n matrices.

A: Given: symmetric  n×nmatrix

Q: Let A be an n xn Hermitian matrix and let æ be a vector in C". Show that if c= xAx, then c is real.

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Q: Let A be a 7 × 5 matrix of rank 4. Let P and Q be theprojection matrices that project vectors in R7…

A: Let A be a 7 × 5 matrix of rank 4. Let P and Q be the projection matrices that project vectors in…