5. (a) Find elementary matrices E; (avoiding ones that swap rows) which will row reduce the matrix 1 2 2 A = 1 1 3 1 to an upper triangular matrix, preferably with 1s on the diagonal. (b) Hence write down an LU decomposition for A.

Q: Let A be a 5 x 5 matrix with det(A) = -10. 1. If the matrix B is obtained from A by adding 4 times…

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Q: find the inverse matrix

A: As per the question, we have to form a 3×3 matrix, given the unique symmetrical elements of YBUS(s)…

Q: a) For invertible matrices A, BER"Xn, show that ((AB)")- = (A-)"(B)".

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Q: A is an n × n matrix with the property that A^2 = A. (a) If B = In − A, show that B^2 = B. (b) Show…

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Q: the given matrix B, =[3 B Show that the matrix B is diagonalizable [Cite any theorems used] Find…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: 21.1f A' = 34² where A is n by n matrix, then (a) A= 31 (b) A 31 if rank((A) =n () A" =!1 (d) a and…

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Q: (a) Let A be a 3 x 3 matrix whose entries on the main diagonal and below the main diagonal are all…

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Q: Find (A, B), ||A||, |B||, and d(A, B) for the matrices in M2,2 using the inner product (A, B) =…

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Q: Consider the bases of R2 B1={(1,0),(1,3)} B2={(0,1),(1,1)} E={(1,0),(0,1)} Correspond M(Id)_B1_E (a…

A: To find a base change matrix from B1 to E, we need to find the linear combination of basis vector in…

Q: a) For invertible matrices A, BE R™×", show that ((AB)")-1 = (A-1)" (B1)". b) Let A, B, C, D e R"*"…

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Q: Let A be a matrix that satisfies ?^2 =? where ? is the identity matrix. a. Find a 2x2 example of…

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Q: rmine which of the following matrices is orthogonal. V3 1 (a) (b) V3 0. V3 1- [1 -1 (c) 1 -1 (d) (e)…

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Q: Let A, B, and C be invertible matrices of the size. Prove that (ABC)" == ("B"A" same size,

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Q: Show that LU decomposition is not possible for the matrix A, where 1 2 3 A 2 4 1 0 2

A: The given matrix is,A=123241-102

Q: Which one of the following equations is true for nxn matrices A, B, and C? (Assume all matrices…

A: For the given matrices A, B, and C. We have to choose the correct option.

Q: 3. Let A, B € Mnxn (F) be n x n matrices. (a) Prove that tr(A + B) = tr(A) + tr(B). (b) Prove that…

A: Trace of matrices is sum of its  diagonal entries

Q: Let B=(b₁,b₂), C=(C₁,C₂), be bases for R² b₁ = (-5,-3), b₂ =(3,2), C₁=(1,3), C₂ = (1,2) Find the…

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Q: (a) If A and C arenxn matrices with C invertible, prove that: det (C-AC) = det(A). (b) Given that…

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Q: Consider the LP problem: Maximize 3xı + 2x2 subject to: x1 – x2 + 2x3 9 3x1 + x2 – x3 0 Find the…

A: Given LP problem is, x1-x2+2x3≤82x1+x2-x3≥6x1+3x2≥93x1+x2-x3≤10x1,x2,x3≥0 The canonical form of LP…

Q: (b) Prove that the following matrices are symplectic : (i) (ii) [1] matrix. where I is the nxn…

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Q: Prove why A-1=(ATA)-1AT is correct using the invertible matrix theorem

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Q: Show that any two rows of a matrix can be interchanged by elementary row transformations of the…

A: The two transformations are as follows:, this means that multiple row 'i' by 'k', this means that…

Q: for a -1 2x +5 f (x) = If fis the function defined above, then f' (-1) is A -2 B 3. E) nonexistent…

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Q: Consider A = 21 2 1 3 -1 -3 4 Convert A to an upper triangular matrix U by using Gaussian…

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Q: Let 3 A = -1 -1 3 -1 -1 3 (a) Find a matrix P that orthogonally diagonalizes A. (b) Find B = P-¹AP…

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Q: 1) Consider the "elementary matrices" 7 01 Elry - [88], Es-in-=[68], and EET-1 (8) E5-123 : 050 =…

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Q: where * denotes a nonzero number. A = LU= = dim(N(AT)) = 1 and dim(R(AT)) = 4 dim(N(AT)) = 2 and…

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Q: Consider the elementary matrix 1 0 -- a 2 1 Describe the action of this matrix from the left in…

A: Here →A=(1,2),→B=(0,1) The vectors A, B are linearly dependent if their determinant is zero. i.e.…

Q: a) Compute the adjugate of the given matrix A and then compute the inverse of the matrix 1 0 2 A = 4…

A: We have to find the adjugate of the matrix A. We know that the adjugate is the synonym of the…

Q: 3. We want to find a matrix B corresponding to a transformation TB (-) such that TB (TA(x)) = R² and…

A: Given : two transformations TA and TB such that TBTAx∈ℝ2 , and TBTAei=0 for i=1,2. where e1,e2,e3…

Q: USE THE SAME MATRIX "E" from above. Verify E x inv(E) is a 4 x 4 Identity Matrix. Fill Up the Empty…

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Q: If matrix A (mxn) has full rank, and I multiply it by its conjugate transpose A*. In other words,…

A: We will give a counter example that will prove this statement wrong.

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

A: Given Quadratic form is  Q=6x12 +9x22 -4x1x2                            ⇒…

Q: Find bases for row(A) and col(A) in the given matrix using A', 1-3 1 A=0 2 3 1-5 -2 row(A) col(A) 11…

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