C: An example of diagonalisation: 1) Find 3 vectors e₁ e2 e3 satisfying the equations : Let T be the operator of C3 with matrix M = =e1 T(e₁) = T(e₂) = ie2 T(e3 = -ie3 2) Find the matrix of T in the basis (e1,e2, 3). 3) Use this to find T4 with as little computation as possible. 2 1+i (1) 0 i 2i 1 0 0

Q: Use the definition of A to write the matrix equation as a vector equation. ΓΟ 1 Ο 11 15 -2 4 9 -3 7…

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Q: Let B, D be the following two bases of R³: B = D= 0 0 -2 2 a) Find the change of coordinates matrix…

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Q: ( 7 ) to ( 2₁ ) ² -Y for M-1 makes sense geometrically. ? Find the inverse matrix of M and explain…

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Q: Let: v = the matrix: -20 -15 11 18 Write v as a linear combination of the vectors in the following…

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Q: 2. Find a nonzero vector that lies in the intersection of the plane {x + 2y + 3z = 0} 1 2 and the…

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Q: - 3 HG 4 4 5 1 2 Let P = - 3 1 3 - 1 W₁ = -5 0 - 4₂ = a. Find a basis (U₁, U₂, U3} for R³ such that…

A: (a)It is given that, P is the change of coordinates matrix from to .Also, the values are:So, using…

Q: Find the vector x determined by the coordinate vector ---(DBE) 8 and the basis B = 0 XB = The vector…

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Q: 9. Show that the following statements about two vectors (a, b), (c,d) = R² are equiv- alent. (a) ad…

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Q: Use the definition of Ax to write the vector equation as a matrix equation. 7 4 2 9 +X3 +x2 HOO -9 9…

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Q: The vectors 3 -4 u = -7 = 12 w = -8 -23 + k are linearly independent if and only if k #

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Q: Use the definition of Ax to write the vector equation as a matrix equation. 3 - 1 +23 + Z4 [HDHIHOI…

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Q: Use the definition of Ax to write the vector equation as a matrix equation. 3 4 - 2 7 -3 + X2 - 9 5…

A: Given vector equation- x13-501+x24-3-99+x3-267-6=7198 To write the vector equation in matrix…

Q: Let A be a 3×3 matrix such that 2 Nul (A) = Span 2 -31 2 is a solution of the matrix equation 0]…

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