Compute the Matrix Function e A where 0 A = [ i and use 0-2 O 3 Ceyley hamilton theory 1

Q: Explain why, no matter how the circuit is completed, Pip must place an even number of additional…

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Q: 7. Let A be an invertible matrix. Prove that if A-¹ = AT, then det(A) = +1.

A: Given: A is an invertible matrix. If A-1=AT, to prove that detA=±1

Q: Let K be an nxn matrix over Z26 such that K = K-1. Explain why either det(K) = 1 or %3D det (K) =…

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Q: Let P: R² → R² be defined by P = projspanuu, where u = Find the matrix associated to P. Enter your…

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Q: Let A = a Show that det (A-\I₂) = λ²−tr (4)\+det(A), where tr (A) =a+d. c d (In general, the trace…

A: We will prove it by expanding determinant along Row 1

Q: let D be a 2x3 matrix being = [ -2 6 4]                                                 [-1 3 h]…

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Q: 2. Matrix A below is a singular matrix, calculate the value(s) of q. A = [3 2²²q] 32- [5 marks]

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Q: 0 Find a non-zero 2 × 2 matrix A such that A? 0 0 A =

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Q: Let u = Let b = 13 - 1 a C and v= 13 1 Show that a C is in Span {u, v} for all a and c. Find the…

A: The given vectors  and .We have to show that the vector  is in the span for all .

Q: Let B be an n X n matr ix and let E be an n X n elementary matrix. Then det(EB) = (det E)(det B)

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Q: Let f(u) = u™ Au, where u e Rd and A e Rd×d is a symmetric matrix. Calculate Vuf(u).

A: Directional derivative: If the function f is differentiable at x, then the directional derivative…

Q: Let [156 A = x 1 y 22-6 Find the value of (x, y, z) so that A is a symmetric matrix. (x, y, z) =

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Q: Let A = P = 3 -10 0 -18] 6 2 9 6 0 11 -2 3 1 0 -2 1 0 -2 Find an invertible matrix P and a diagonal…

A: The given matrix is;  A=[ -10 0 -18           6  2   9          6   0   11]