Let A be the following matrix 4 5 3 6 4 8 2 4 3 After diagonalization, Pand Dare found such that A = PDP !Find the trace of D.

Q: Let A be the following matrix 1 7 4 9 4 7 3 4 3 After diagonalization, Pand Dare found such that A =…

A: We use the following theorem: If A and B are two square matrices of order n, then trace of…

Q: Consider the 6 × 8 matrix 3 0 0 0 0 1 2 1 0 0 0 0 1 0 0 -3 4 -7 -9 A = 0 0 0 0 0 0 0 0 0 1 8 1 and…

A: The main objective is to answer the sub parts by using given matrix which is in reduced row echelon…

Q: Find the elementary matrix E such that EB = A where %3D 2 3 1 2 3 1 A = 4 -3 -2 and B = -8 6 4 7 -6…

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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 0 2 -1 0 2 0 1

A: Given the matrix A=1020-10201 To find an orthogonal matrix P and a diagonal matrix D such that…

Q: . Given the matrix A below, alue for det in A A = 1 0 2 2 0 0 2 1 1 10 1 0 1 4

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Q: Let A be an m × n matrix. Show that A is row equivalent to O if and only if A = O .

A: Consider the given information as A be an n×nmatrix

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Q: Consider the Az 1 34 17 9 203 2 8 16 6 0 5 /

A: (a) We know that we can find the determinant of the matrix by expanding along any column or row.…

Q: Consider the following matrix A, where 0 -4 -6 0 -3 A = -1 1 2 5 Find an invertible matrix P and a…

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Q: Find a QR factorization of the matrix in the given exercise.

A: Find a QR factorization of the matrix 11101-120-11001510

Q: Find the charo cteristica poly no nomi the matrix A = 3. 3. /- P(x) = 1.

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Q: Let a matrix '2 -2 1 A 2 3 1 1 -2 - 2 2 Show that A"A = I and deduce that AT = A-1.

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Q: Let A be the following matrix 6 5 3 4 5 9 3 1 4/ After diagonalization, P and Dare found such that A…

A: The solution is given as

Q: Find an LU factorization of the matrix A (with L unit lower triangular). 4 - 4 2 - 8 2 - 1 A = 10 8…

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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: Let A be the following matrix 5 8 5 5 9 1 After diagonalization, Pand Dare found such that A =…

A: To find the trace of D we will use the fact that some of eigenvalues of a matrix A is equal to its…

Q: Let A = diagonalizable matrix( A = XDX-1), then X and D are: LO H O4

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Q: (a) Let A be an m × n matrix, and let B be the result of performing a single elementary row…

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Q: Find a diagonal matrix D and a nonsingular matrix P such that D= P-'BP.

A: A matrix is a mathematical object containing numbers arranged in rows and columns. The eigenvector…

Q: Let A be an nxn matrix, then for any n EZ*, det( A")= (det A)" . Select one: True False

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Q: If A is a square Matrix such that A'-A, what are the possible values of det A?

A: Determinant possible values

Q: (i) Use the properties of trace to argue that tr(AʼA) = tr(AA') for any n × m matrix A. [2 0 (ii)…

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Q: Let A be the following matrix 6 7 4 9 5 9. 3 4 After diagonalization, P and 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: Identify a matrix P that diagonalizes 2 6 A = a. 1 P = - 2 Ob. P = -1 0 0 2 Oc. P = 01 1 2 O d. -2 P…

A: Solution

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…

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Q: Let A be the following matrix 7 4 4 4 After diagonalization, P and D are found such that A PDP !Find…

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Q: Let A =mnd B- then the matrix (2AB + A")" is equal to O None of these O equal to the above 2 17

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Q: Let B be a 5 x 5 matrix such that each row of B contains every number from the following list…

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Q: Let A be an m × n matrix and let B be an n × p matrix. (a) Prove that Col(AB) C Col(A). (b) Use part…

A: i have given the formulas what i have used and where i have used

Q: Let A be the following matrix 6 5 3 4 5 9 3 1 4 After diagonalization, Pand Dare found such that A =…

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

Q: Let A be the following matrix 9. 1 9. 3 2 4 After diagonalization, Pand Dare found such that A =…

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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: Let A be a nonsingular matrix. If det(A)=3, then det(A) = %3D

A: In this question we have to find detA-1.

Q: Suppose that A is an n × n matrix and det A + 0. Determine the rank and nullity of A.

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Q: Let A = 0 1] 3 03 0 0 2 = If possible, construct P and D such that A don't need to compute P-¹).…

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Q: Find a Matrix P that nationalizes A, and check your answer y computing PDP¯1 0 00 0 0 0 30 1

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Q: Show that if A is an n × n matrix, then det(AAT ) ≥ 0.

A: Given, A is a n x n matrix. Let AT be the transpose of A. To prove det (AAT) is non-negative.

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

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Q: Let A be the following matrix 6 7 4 9 5 9 1 3 4 After diagonalization, P and D are found such that A…

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

Q: O Let A be an m x n matrix, and let B be the result of performing a single elementary row operation…

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Q: (a) Let A be an m × n matrix, and let B be the result of performing a single elementary row…

A: We have to prove that following Statement.

Q: et A be the following matrix 2 7 2 4 4 8 2 3 3 fter diagonalization, Pand Dare found such that A =…

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Q: Suppose A is a 5 by 5 matrix with det(A) = 6 What is det(AT A)? Answer:

A: Given det(A) = 6

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.

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Q: Let A be the following matrix 2 8 4 448 353 After diagonalization, Pand Dare found such that A = PDP…

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

Q: Consider the matrix 1 A = 1 1. Compute exp A. 2. Verify your calculation above using the identity…

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Q: If A is an invertible matrix and det(A) = 7, what is det (A-1)?

A: Given: If A is an invertible matrix and det(A) = 7 To find: what is det (A-1 )?