Final answer:
To solve the equation am + bh = r, substitute the given values for m, n, and r. Use vector addition and solve the resulting equations to find the values of a and b.
Step-by-step explanation:
To solve the equation am + bh = r, we can substitute the given values for m, n, and r. Given that m = (-3,2), n = (0,4), and r = (-6,0), the equation becomes a(-3,2) + b(0,4) = (-6,0).
Using the properties of vector addition, we can rewrite the equation as (-3a, 2a) + (0b, 4b) = (-6, 0).
By equating the corresponding components, we get two equations: -3a + 0b = -6 and 2a + 4b = 0. Solving these equations simultaneously will give us the values of a and b.