2 1 A 2 1 2 2 2 1, Find an orthogonal matrix P and a diagonal matrix D such that A = PDPt.

Q: Find an LU factorization for the matrix A = -2 3 4 1 -3 0 2 3-2, Verify that LU = A.

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Q: Express the invertible matrix (1 2 1 10 1 1 2) 1 as a product of elementary matrices.

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Q: Let B = {1, cos t, cos? t, cos t, cost t} and C = {1, cos t, cos 2t, cos 3t, cos 4t} and assume the…

A: Given B=1,cost,cos2t,cos3t,cos4t and…

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 (x, y, z) E R³ and the transformation T: R³ → R² be given by T(x, y, z) = (2x + 4y, x + 3y + z).

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Q: Express the matrix A = as the product of elementary matrices. 1 2 2 10 2 31

A: Elementary square matrix :- A square matrix of order n is said to be an elementary square matrix if…

Q: Prove that (A + B)² = -(A + B) in matrix..

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Q: Find an orthogonal diagonalization for A = 1 0 1 0 1 -1 (1888) -1 1 i.e. find an orthogonal matrix U…

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Q: Find the characteristics equation of the matrix [1 2 A -2 -1 01 and hence find A-.

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Q: Diagonalize the matrix 1 0 A = -2 3 -1 -2 0 2 In other words, you need to find a diagonal matrix D…

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Q: 2. Diagonalize the matrix using normalized vectors. B= 3 1

A: Given,        B=1331

Q: the matrix A = and explain why or why not this matrix is diagonalizable

A: In the given question, concept of diagonalizable matrix is applied. Diagonalizable Matrix Any square…

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: Find two non zero matrices A and B such that AB = 0. %3|

A: Find the two matrix which satisfy the given condition

Q: 5 3 [B] -5 -6 i.e. write A = LU where L is a lower triangular matrix with 1's on the diagonal, and U…

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Q: What is the condition for a diagonal matrix to be orthogonal?

A: use the properties of orhtogonal with respect to a diagonal matrix...

Q: Diagonalize the matrix -5 -2 A = 3 [ by writing it as A = PDP-1

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Q: Let -1 1 A = -1 1 -1 -3 3 Find an upper triangular matrix which is orthogonally similar to A.

A: An upper triangular matrix is a triangular matrix with all elements equal to below the main…

Q: Let y = and u= 3 Write y as the sum of two orthogonal vectors, one in Span {u} and one orthogonal to…

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