Consider the matrix A = 0 0 0 0 a = 4 -2 a a 8 a=-4 a € R\{-4,4} A is invertible for any a ER with a € R. Select all values for a such that A is non-invertible.

Q: Find an invertible matrix P and a matrix C of form that A PCP-¹. = P = C = −2+ i -2- i 2 2 3+2 i 0…

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Q: Find a matrix A such that 5 ¹0-08-08-0 A 5 A A = A =

A: We can solve this as follows:

Q: Diagonalize matrix A, i.e., find diagonal D and invertible P such that A = PDP-1, where -[:] 3 2 A =…

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Q: let Amxn matrix , c scalar If cA=0, then Select one: a. c=0 and A=0 b. c=0 or A=0 C. C0 or A=0

A: WE have to check the meaning of cA=0.

Q: _Let A = -3 -1 1 2 -12 0 0 -1 5 If possible, find an invertible matrix P so that D = P-¹AP is a…

A: Let us strat by finding the eigen values of the matrix…

Q: Given the vector x = (1, 2, 2)T , find a Householder matrix that will zero out the last two entries…

A: Given: Vector, x=1, 2,2TTo find: Householder matrix H

Q: Let A be any invertible 9 x 9 matrix. Which of the following is equal to det(Adj A)? OA. (det A) B.…

A: Given: A is an invertible matrix of order 9×9 We are required to find: det(AdjA)

Q: Consider an n x n matrix. Give 3 equivalent conditions for A to be invertible

A: Let A be an n×n matrix. we have to give 3 equivalent condition for A to be invertible. Conditions…

Q: Let A = [5 0 X = 5 Find an invertible matrix X and a diagonal matrix D such that X-¹AX = D. 001 D =…

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Q: Let A be a 3 x 3 symmetric matrix given by A = 2 -1 0 -1 0 2 -1 2 -1 Find an upper triangular matrix…

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Q: Let A = 3 ů 5. positive definite show that the matrix A is. پول و مع دول ۷۵

A: A matrix is said to be positive definite if the given matrix is symmetric and all its eigen values…

Q: Let A be a symmetric positive definite n×n matrix and let S be a nonsingular n × n matrix. Show that…

A: To show that STAS is positive definite, we need to prove two things: 1. STAS is symmetric. 2. For…

Q: If A=XDX−1 where  X is a diagonalizing matrix of A, then 7X is also a diagonalizing matrix of A.…

A: Given: Where, X is a diagonal matrix of A, then 7X is also diagonalizing matrix of A. To determine:…

Q: Suppose A is a 2 x 2 matrix such that A and 1 A What is A-1?

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Q: Le+ A=22 1 Find on orthogonal matrix Q and a 2-1 diagonal matrix D such that A=QDQT.

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Q: Find an invertible matrix X and a diagonal matrix D such that X-1 AX = D. You don't need to compute…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: For which value of x is the following matrix not invertible: 1 1 2x A = 1 2x 2x 2x 2x 2x 4 1 -1 1 2

A: For a matrix A to not be invertible: dat(A) = 0.

Q: Find a 3 x 3 matrix A such that Az = 10 for all i in R³. A =

A: Given Ax=10x  We have to find 3×3 matrix A  Now

Q: Use matrix algebra to show that if A is invertible and D satisfies AD=1, then D = A.

A: Given: A is invertible and D satisfies AD=I. To show: D=A-1 Proof: We have equation AD=I.…

Q: Find matrices P, D and P-1 that diagonalize matrix A, where A = P = D= P-1 20 0 -11 -2 -3 -30 -1

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Q: TRUE or FALSE: Every invertible n xn matrix is similar to the identity matrix In.

A: To state true or false given statement.

Q: Exercise 5K. What must be true about n so that an n x n matrix A satsifies det(-A) = -det(A)?

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Q: (4) Find an orthogonal matrix P that diagonalizes A. Verify that PT AP gives the proper diagonal…

A: As per the question we are given a 4×4 square symmetric matrix A and we have to find an invertible…

Q: Let a be a real number. Let 1 1 A = | 0 1 1 1 1 2 a) Find the value of a for which the matrix is not…

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Q: e a square Fits diagona diagonal ele anal the val

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Q: 2 6 -0 Consider the matrix A = 0 5 -2 00 4 If the matrix is diagonalizable, diagonalize it, that is,…

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