Let A= P = N -8 16] -8 14 8 Find an orthogonal matrix P with rational entries and a diagonal matrix D such that D = PTAP. 16 8 2 N ∞ , D =

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: A) Justify if the matrix A is diagonalizable.B) Find a matrix T and a diagonal matrix J, such that…

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Q: Let B=(b₁,b₂), C={C₁,C₂), be bases for R² b₁ = (-1,2), b₂ = (1, -1), C₁=(1,2), C₂ = (1,1) Find the…

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Q: Suppose that Q is an orthogonal matrix, then OaQ-8 ObQ-2 d 1Q-0

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Q: det (–3(A" A-²)*) Consider matrix A of order 3, the value of corresponds to: 1 a) –7 - 1 b) –3 c) –3…

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Q: Find the projection matrix P, and the projection of b= (1,2,3) onto 2. Let A= -1 -1 the column space…

A: Given matrix is A=1001-1-1

Q: For the matrix M M. [1 -2 -2] 0-5 3 -11 -4 F find three different non-zero vectors that are in the…

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Q: 1 A = )Find the rank of a matrix 7 17 1 - 2 | 3.

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Q: Let B=(b₁,b₂), C=(C₁,C₂), be bases for R² b₁ = (-5,-3), b₂ =(3,2), C₁=(1,3), C₂ = (1,2) Find the…

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Q: s elect the matrix correspon ding to the form QLX,, Xz, Xx, Xu ) = - 2x1²+ 5 X; - 7×3 -4 Xú - 6Xi Xz…

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Q: Find a QR factorization of the matrix A. [-6-12] 17) A = 17) A 3 36 0-12 18) A- 01 1 10 -1-11

A: We have to find the QR factorization of the matrix

Q: Let B1 = {T1,t2, t 3} and C, = {w1, w2, w3} be two bases for R³ such that । = - , के = - े;, के; =…

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Q: Diagonalize A the matrix A. -27 2 3 4 3+ i√5 0 0 [S+W³² $ "VE] [3+1 0 3-i√√5 i√5] 0 0 [-³+1 0 O…

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Q: -11 36| and P 10] 3 2. Find the diagonal matrix of A = -3 answer -21

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Q: 7 Let y = and u Write y as the sum of two orthogonal vectors, one in 5 4 Span {u} and one orthogonal…

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Q: 1 -4-2) s) Let A := -2 3 2 4 -8-5 (a) Show that A is diagonalizable and find a nonsingular P such…

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Q: Let W be the set of all vectors of the form [3s 4r5t] 2r + 2s - t 3s - r + 5t 3r + 2s + 4t with r, s…

A: The set ( W ) consists of vectors that can be formed by linear combinations of the vectors with…

Q: Let 2 -1 A = 1 -1 0 2 Find an orthogonal matrix P and a diagonal matrix D such thatt D = P"AP. D =…

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Q: Verify by finding the matrix of S 0 T (a) by direct substitution and (b) by matrix multiplication of…

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Q: Find the change-of-coordinates matrix from B to the standard basis in R". 2 -2 3 8 -2 7 8. Pa

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Q: Let W be the set of all vectors of the form with r, s and treal. Find a matrix A such that W =…

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Q: Enter the matrices P and D below.

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Q: P = ) Let A = -15 -8 -8 0 -3 0 24 16 13 Find an invertible matrix P and a diagonal matrix D such…

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Q: Let M = -3 2 -3-2 M³ + c₁M² + c₂M + c3I3 = 0, where I3 is the identity 3 x 3 matrix. C1 || S || C3…

A: Here the matrix is given by M=-11-3-3232-32 Here the equation is given by M3+c1M2+c2M+c3…

Q: Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal mama Da 15) 10-61…

A: The given matrix is                                      10-6-65

Q: d) All of the above LQ9. Suppose A is the 4 by 4 identity matrix with its lAst column renoved. The…

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Q: Give an example of a 2 x 3 matrix A that is in RREF and whose solutions to 2 -(-) 4 Ax = 0 is…

A: Introduction: Systems of linear equations can be solved using a type of matrix called reduced row…