7 20 -10 Let A = 20 7 10 Find an orthogonal matrix P with rational entries and a diagonal matrix D -10 10 22 such that DPTAP.

Q: TRUE or FALSE: If A, B, C are square matrices such that CA = CB, then A = B. TRUE FALSE

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Q: Г1 2 3 4 5 A = 5 0 2 4 6 8 5 5 5 5

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Q: Find a QR-factorisation of 1 1 -1 1 | 1 1 1 1 0 -

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Q: [2a11 5a12 Let A = |2a21 5a2 -3a23 2a31 5a32 -3a33 diagonal matrix and neither B or D is equal to…

A: The given matrix isA=2a115a12-3a132a215a22-3a232a315a32-3a33.We have to factorise A into A=BD where…

Q: Assume that the matrix A is row equivalent to the matrix B where A = 1 1 -3 7 9 -9 without…

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Q: the matrix 9 8 16 6-18 -16] by writing it as A = PDP-¹ Diagonalize -3 A-6 18 P = JUL

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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: Find the LDU factorization of L = That is, write A = LDU where L is a lower triangular matrix with…

A: Given We need to find the LDU factorization of matrix A.

Q: Let A = P = [-25 4 -19 4 4 8 4 8 . Find an orthogonal matrix P with rational entries and a diagonal…

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Q: Which of the following statement is correct? a. R= I3x3 can be a rotation matrix b. Rotation matrix…

A: Please find the answer in next step

Q: Find the LU factorization of A = 10 -15 -21 That is, write A = LU where L is a lower triangular…

A: Given: 55108-15-21

Q: a) Decompose the coefficient matrix A into lower and upper triangular matrices.

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Q: 15. Diagonalize the matrix A = 11 expressing it similar to a diagonal matrix D. "

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Q: Find a 2 x 2 matrix such that (199-41 188- 6 6 2

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Q: Orthogonally diagonalize the matrix 1 2 2 -2

A: Given,     122-2

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: Use the fact that matrices A and 8 are row-equivalent. 2 10 0 5 11 0 722-2 A = B = 1 2 3 10 23 7 0…

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Q: agonalize A and use the diagonal matrix to compute A100

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Q: 1.Solve the following polynomial equations.  a)  2X3+1=x2+2X

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Q: Orthogonally diagonalizable the following matrix 2 1 1 C = -1 1 1 0 -1 1.

A: The solution is below.

Q: Construct a 3x5 matrix A such that dim Nul 4. Explain and justify your answeT.

A: We need to construct a 3x5 matrix A such that dim Nul A = 4. So, nullity(A) = dim Nul A = 4. We know…

Q: 4 = = - (13 + 2) 0 3 13 -13 13 + 2 0 9. 1 B = 1 13 +3 4 -(13+ 4) [13 13+1 1 0 Calculate the…

A: Matrix multiplication is defined as row by column multiplication where the elements of the ith row…

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: Let A and B be the matrices as shown. '1 2 1 1 2 1 ^ - ( ²³ ) ·- - 6 ÷ ³) A = 0 5 1 B = 2 -1 4 2 −1…

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Q: 1 3 (b) If possible, express A = 2 3 product of elementary matrices.. as a

A: The given matrix is A=1323.

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT 6. A small metal bar, whose initial temperature was 20°C, is…

A: Given,Initial temperature is .Then,Then, by the formula of of Newton's law of heating we…

Q: True or False. Why? An expression of an invertible matrix A as a product of elementary matrices is…

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Q: Find a basis for the column space of -2 4 4 A = 3 3 4 -2 -16 -8

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Q: Enter the matrices P and D below.

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Q: A B 0 D where A, B, D are 2 x 2 matrices and 0 is the 2 × 2 zero matrix. Prove that det(M) det (A)…

A: Given : M=AB0D  where A, B , D are 2×2matrices and 0 is the 2×2 zero matrix. To prove : det(M) =…