Question: Write down the compatibility conditions on the following systems of linear equations by first computing a basis for the cokemel of the coefficient matrix. (a)

Write down the compatibility conditions on the following systems of linear equations by first computing a basis for the cokemel of the coefficient matrix.
(a) 2x + y = a. x + Ay = b, - 3x + 2y = c;
(b) x + 2y + 3z = a, - x + 5y - 2z = b, 2x - 3 - y + 5z = c;
(c) x1 + 2x2 + 3x3 = b1, x2 + 2x3 = b2, 3x1 + 5x2 + 7x3 = b3, - 2x1 + x2 - 4x3 = b4;
(d) x - 3y + 2z + w = a, 4x -2y + 2z + 3w = b, 5x - 5y + 4z + 4w = c, 2x + 4y - 2z + w = d.

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