4. Find a diagonal matrix A that satisfies the given condition. 16 At = 0 81 0 1. 01

Q: 2 Suppose A = is positive semi definite matrix then: a 10 O a. Jal < 20 O b. a <-v20 Oc lal < v20 O…

A: Suppose A=2αα10 is a positive semidefinite matrix then which of the following is correct.

Q: How many free variables does each augmented matrix have? 10 8 01 9 0 0 0 -3 Select an answer b. 1 0…

A: Answer

Q: Find the elementary matrix E such that EB = A where %3D 5 4 1 ] 4 1 A = |4 |7 -6 1 -1 and B = |12 3…

A: EB=A multiplying with B-1 on both sidesEBB-1=AB-1E=AB-1

Q: 1) Construct the matrix A =(a;;) where 3x2 ) aj = i+j, if i = j,and Li-j, if itj %3D

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Q: The mist Consider ann x m matrix A. Find dim(im(A)) + dim(ker(A")), in terms of m and n.

A: Please check step 2 for the solution.!

Q: 2. Let n x n matrix A have the form Au Azz A = where An is k x k (where k < n). Show that A is…

A: The given matrix is  A1100A22 A matrix is called non-sigular if the value of its determinant is…

Q: (16) Which of the following is a symmetric matrix? (Select all correct answers) ro 1 21 O1 0 1 l2 0…

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Q: [3 Compute the natrix exponential e4t for the diagonal matrix A = !!

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Q: Decompose the given matrix as indicated: [25 5 4 10 8 16 = 1 0 0| 41 12 13 l21 C31 32 1 1 0 0 12 22

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Q: e) Let A be an n x n matrix. If det(A – AIn) = 0 for some ) e R, then det(A² – X²In) 70.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find the elementary matrix E such that EB = A where 3 1 2 3 1 A = |2 -1 -1 and B = |4 -2 -2 7 -8 4 7…

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Q: 3 91 Given a matrix A3 9 6 7] which of the elements aij follows the condition i=j. 9,9,1

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Q: Find the elementary matrix E such that EB = A where 3 3 3 -12 A 3 -1 -2 and B 4 8. 8 -7 3 8. -7 3 |…

A: The inverse of a matrix can be calculated by following steps  1 calculate the minor for the given…

Q: Thich of the following is a non-singular matrix P such that PAP is diagonal if 7 0 ? -4 2 A =

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Q: (4) Let A E R™xn be any matrix. Solve the following problem min ||AX – I||r Hint: Write X = [x1,...,…

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Q: Find the elementary matrix E such that EB = A where 4 1 4 4 1 3 -1 -2 and B 18 -6 -12 %3D 5 -7 4 -7…

A:

Q: Suppose that A is an m × n matrix and satisfies the following conditions: dim(row(A)) = 3…

A:

Q: 5. Compute the condition number K(A) of the following matrix 1 1+€ 1 1 1 A 1 1 1 1+€ What is k(A) as…

A: Conditional number is κ∞(A)=∥A∥∞·∥A-1∥∞.If matrix A is known to us so ∥A∥∞ is easy to find .First…

Q: Let A be the following matrix 4 5 3 6 4 8 2 4 3 After diagonalization, Pand Dare found such that A =…

A: Use the following theorem: If A and B are two n by n matrices, then trace of (AB)=trace of (BA)

Q: **15. Suppose A is an m × n matrix and x e R" satisfies (AA)x = 0. Prove that Ax = 0. (Hint: What is…

A:

Q: 7 Show that A = 13 and B = 4 2 are similar matrices by finding an invertible matrix P satisfying 2 A…

A: Given,A=7-132-4 abd B=1-2-22Let,P=abcd , and P=ad-bc=nSo, P-1=1nd-b-ca where n=ad-bc=dn-bn-cnan

Q: 4. Decide if there is a three by three matrix A such that A. 1 for all æ, y, z in R.

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Q: 9. . Suppose that A = PDP¯' and B = 31 + 2A + A². 5 Let D a Find a diagonal matrix D1 such that B =…

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Q: Find the elementary matrix E such that EB = A where 4 1 2 4 6. 1 A = 2 -3 -1 and B = -4 2 6 -8 -8 2…

A: To find E such that EB = A

Q: 2. Decompose the given matrix as indicated: [25 5 4] 10 8 16 8 12 22 1 Answer:

A:

Q: 22 Nove If the matriX A is m x n and Ar b is solvable for every b then a m<n b elimination results…

A: This question is related to Linear Algebra

Q: 7. The rank of an identity matrix of order n is: А. п - 1 В. п C. n+1 D. 0

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Q: Let A be the following matrix 3 7 4 8 4 7 1 2 4, After diagonalization, P and D are found such that…

A:

Q: For a matrix A having JA| = 0, which of the following are true? * O A- exists with |A¬' |= 0| O A-…

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Q: 1 1 1 A =1 1 1 1 2 1 . How many nonzero elements are there in the adjoint matrix of matrix A?

A:

Q: A is akxl matrix with rank r and nullity n. If 2r + n = 10 which of the following cannot be the…

A: it is an application of rank nullity theorem.

Q: 3. Show that for any n x n matrix A of rank r, we have ||4|| < ||4||ES VFl|4||.

A: To show that: A≤AF≤ rA  for any n×n matrix A of rank r.

Q: (4) Given matrix A = G ). and that h(T) = T² – 2T – 7, find h(T).

A:

Q: Find an elementary matrix E that satisfies the stated equations. 8. 1 5 8 5 8. 1 5 B = 2 -7 D -6 21…

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Q: What matrix E puts the matrix A into an upper tr 4= U? Show your work! 210 042 A =

A: Introduction: In linear algebra, LU Decomposition, also known as lower–upper (LU) decomposition or…

Q: d the third column of A 'without computi 1 be found without computing the other om nted matrix (A…

A: The matrix is given as A=-2-3-2525431218. To determine the third column of A-1 without computing the…

Q: Find the Frobenius norm of the given matrix. 15 A = 15 15 ||A|| = Ex: 6

A: The frobenius norm is calculated as:

Q: Find the elementary matrix E such that EC = A where 3 3 -3 1 3 3 1 A = -1 and C = 2 -3 | 8 -7 2 23…

A:

Q: 1 0 21 21 4. If M = -1 3 4 and B: = 3 4 078 L5 61 Find the matrix C such that MC = B.

A: To find- If M = 102-134078 and B = 123456 Find the matrix C such that MC = B

Q: 5). (4) Given matrix A = and that h(T) = T2 – 2T – 7, find h(T).

A:

Q: 3. Consider the following matrix C 3 1 -1 A = 1 4 1 -1 1 5 b) Find the Cholesky factorization A=GGT.

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Q: Find k for which the matrix below is NOT invertible. 1 1 3 -1 2 1 k

A: For matrix to be non-invertible, it's determinant must be 0. We will use this property to find the…

Q: Find the elementary matrix E such that EB = A where 2 1 3 1 A = |4 -1 -2 and B = –16 4 8 9 -7 4 9 -7…

A:

Q: 2. Given the matrix A below, solve for det inv A. A = 1 0 2 ¹2 0 0 11 2 1 1 1 0 1 0 1 4

A: Here we have to use the row operation method.

Q: (3) Consider the matrix [1 k 31 A = 2 4 -6 2 For what values of k is A invertible?

A:

Q: 8. If A is an mx n matrix, wh

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

Q: Find the elementary matrix E such that EC = A where %3D 4 4 A = |3 -1 and C = 3 0. -1 9 -8 19 0 4 ?…

A:

Q: 4. (a) Show that the following matrix is diagonalizable. (b) Find a matrix P that diagonalizes A.…

A: A matrix is said to be diagonalizable if the algebraic multiplicity of the eigen value is same as…

Q: 21 1 2 1 ol -1 A = | 0 2.

A:

Q: (4) Given matrix A= and that h(T) = T – 2T – 7, find h(T).

A: