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If A= [ array cc 1 & -2 4 & 5 array ] ; f(t)=t^2-3 t+7 then f(A)+ [ array cc 3 & 6 -12 & -9 array ]=

Options

  1. A[ array ll 1 & 0 0 & 1 array ]
  2. B[ array ll 1 & 1 0 & 0 array ]
  3. C[ array ll 0 & 0 0 & 0 array ]
  4. D[ array ll 0 & 1 1 & 0 array ]

Correct answer

C. [ array ll 0 & 0 0 & 0 array ]

Step-by-step solution

Given A = bmatrix 1 & -2 4 & 5 bmatrix and f(t) = t^2 - 3t + 7 . First, calculate A^2 : A^2 = bmatrix 1 & -2 4 & 5 bmatrix bmatrix 1 & -2 4 & 5 bmatrix = bmatrix 1(1) + (-2)(4) & 1(-2) + (-2)(5) 4(1) + 5(4) & 4(-2) + 5(5) bmatrix = bmatrix -7 & -12 24 & 17 bmatrix Next, calculate f(A) = A^2 - 3A + 7I : f(A) = bmatrix -7 & -12 24 & 17 bmatrix - 3 bmatrix 1 & -2 4 & 5 bmatrix + 7 bmatrix 1 & 0 0 & 1 bmatrix f(A) = bmatrix -7 & -12 24 & 17 bmatrix - bmatrix 3 & -6 12 & 15 bmatrix + bmatrix 7 & 0 0 & 7 bmatrix f(A) = b

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