Define the function T : R3 → R4 according to T (x, y, z) = (2x − 3y + z, 4x − z, 3x + 7y − 8z, −x + 6y + 5z). (a)Evaluate T (2a, 3a + b, b − 2c), where a, b and c are arbitrary real numbers. (b) Find a matrix A such that T (v) = Av, where v is a column vector.   please provide details

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Q: (c) Consider the quadratic form f(x1, x2, x3) = 3(a₁x₁ + a2x2 + a3x3)² = 4(b₁x₁ + b₂x2 + b3x3)². (i)…

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