Find the companion matrix of p(x) = x2 -7x + 12 and then find the characteristic polynomial of C( p).

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Q: Let Q(x) = 7x} +x} +7x} – 8x1x2 – 4x1x3 – 8x2x3. Find a unit vector x in R3 at which Q(x) is…

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Q: Suppose that an nxn matrix A has a QR-decomposition where

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Q: Let A be an invertible 3 by 3 matrix. Assume that PA²P-15ATA². = Then det(A) =

A: Step 1:   Step 2: Step 3: Step 4:

Q: If you know all 16 cofactors of a 4 by 4 invertible matrix A, how would you find A?

A: Given, an invertible square matrix A of order 4, and we know all the 16 cofactors of this matrix.…

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Q: Let R2x2 be the set of all 2x2 real matrices and consider function phi : C --> R2x2 given by…

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Q: Determine the characteristic polynomial of the matrix 1 1 0-1 0 2x 1 0 0 0 1 A= = 1 X 2 0 X Find the…

A: To find the characteristic polynomial of a given matrix A, you need to compute the determinant of…

Q: Explain why det (BPB¯¹) = det(P) for any matrices P and B. Assume both sides of the equation are…

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Q: Consider the operator R2 → R2 given by left-multiplication by the matrix: B =[6 −7,       1 −2].…

A: Given that the operator R2 → R2 given by left-multiplication by the matrix: B = 6-71-2 We have to…

Q: Find a 3 x 3 matrix A (with real number entries) whose characteristic polynomial is det(A – rls): *…

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Q: 2. Prove Cayley-Hamilton Theorem for a diagonalizable matrix, A: Let A be diagonalizable and p(x) be…

A: Proof for p(A)=0

Q: 6 Let ---B = -8 by T(x) A - a 1 b₁ 8-0- a2 X b₂ az b3 = v x x. = a₂b3-a3b₂ a3b — abვ La₁b₂-a₂b₁_ 3…

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Q: APPLY A SERIES OF ROW OPERATIONS ONTO THE GIVEN MATRIX "A" TO FIND ITS INVERSE. [ A|1] => [ I|…

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