Find the characteristic polynomial of the following matrix using either a cofactor expansion or any other method: [-1 0 1] A =|-3 4 1

Q: B = [3 {[9][9]} 02 4 0 56

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Q: Find the (1, 1) entry of the matrix product XY using the matrices below: a X = b and Y = | c 1 -1 d…

A: To find  entry of the matrix product  using the the matrices below. and  and , and .

Q: Let A = 1 -X -X X 1 -x X X -1 Find x such that A is invertible.

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Q: Write  a formal proof for the given statement. (a) Let A and B be a n × n matrices. Suppose that A…

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Q: Mark each statement as TRUE or FALSE. For every square matrix A we have det(24)=2 det(A). O True…

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Q: v. This theorem provides a new method for finding inverses when they exist: substitute the matrix…

A: Answer

Q: The characteristic polynomial of the matrix A: · PA (A) = x² - 15+8 · PA (λ) = x² - 81+13 ·PA (λ) =…

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Q: Find all (real) values of k for which A is diagonalizable

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Q: Ak = PDP-1 (a) Show by mathematical induction that for a n x n diagonal matrix D with diagonal…

A: Let us prove the given result by induction or by taking induction on order of diagonal matrices.

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

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Q: (d) Is the matrix [2]12 [112] [-112 [2]12 a unit in the ring M2 (Z12)? Justify your answer.

A: (d)

Q: State and prove the : The characteristic polynomial of any diagonalizable linear operator T splits.

A: We have to prove that: The characteristic polynomial of any diagonalizable linear operator T splits.

Q: Suppose C is the code over F2 = GF (2) generated by the generator matrix1 0 1 1 1 0 00 1 0 1 1 1…

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Q: 11. 400 5 32 -2 02.

A: Definition of characteristic polynomial