solve for a, b, and c in the following equation:

Question

2.(a, 3, c) + 3(c, 7, c) = (5, b+c, 15)

Answer 1

2.(a, 3, c) + 3(c, 7, c) = (5, b+c, 15)

Treat the above as a vector equation.

2.(a, 3, c) + 3(c, 7, c) = (5, b+c, 15)      multiply in the two factors

(2a, 6, 2c) + (3c, 21, 3c) = (5, b+c, 15)    add the 1st two vectors

(2a + 3c, 6 + 21, 2c + 3c) = (5, b + c, 15)

(2a + 3c, 27, 5c) = (5, b + c, 15)      now, match corresponding elements

2a + 3c = 5   -------- (1)

27 = b + c  ---------- (2)

5c = 15   ------------- (3)

From (3), c = 5. Substitute for c = 5 in (1) and (2), giving

2a + 15 = 5   -------- (4)

27 = b + 5  ----------- (5)

From (5), b = 22. From (4), a = -5.

Answer: a = -5, b = 22, c = 5