3. Determine whether the following system of equations have no solutions, one solution or infinitely many solutions. a) $-10x_2 + 28x_4 = 5$ $4x_1 + 6x_2 - 8x_3 = 10$ $10x_1 + 7x_2 + 3x_3 + 8x_4 = 9$ b) $-x_2 + 5x_5 = 4$ $4x_1 + 6x_2 - 8x_3 + 10x_5 = 10$ $10x_1 + 7x_2 + 3x_3 + 8x_4 + 2x_5 = 9$ $-20x_1 - 10x_2 + 3x_3 + 15x_4 - x_5 = 20$ 4. Assuming that $1 + 2 + 3 + ... + n = an^2 + bn + c$, find a, b and c by substituting any 3 natural numbers and setting up a system of equations in a, b and c.
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This equation can have either no solutions, one solution, or two solutions. For the second equation, we have a cubic equation (4x + 6x^2 - 8x^3 = 10). This equation can have either no solutions, one solution, or three solutions. For the third equation, we have a Show more…
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