Question: How do you start this? Suppose that a, b, c are integers between 0 and 999 inclusive, and let their decimal repre- sentations be a

How do you start this?

Suppose that a, b, c are integers between 0 and 999 inclusive, and let their decimal repre- sentations be a = ala203, b = b1b263, C = CIC203. For example, if a = 56, then al = 0, a2 = 5, and a3 = 6. Assume that 7 divides a, b, and c. (2) By performing suitable row operations, show that 7 divides the determinant a1 b1 C1 a2 62 C2 a3 63 C3 (ii) Suppose, in addition, that the vectors [a1, a2, a3], [b1, b2, b3], and [c1, C2, (3] are linearly independent and that the parallelepiped they determine has volume equal to an even positive integer less than 25. What is the volume? Explain

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