Final answer:
To find the values of a and b such that v = au bw, substitute the given values of u and w into the equation and solve for a and b. The values of a and b that satisfy the equation are a = 5 and b = 3.
Step-by-step explanation:
To find the values of a and b such that v = au bw, we can substitute the given values of u and w into the equation and solve for a and b. Since u = 1, 2 and w = 1, -1, we have:
v = a * 1 * 1 + b * 1 * 1 = a + b = 8
v = 2a - b = 7
By solving this system of equations, we can find the values of a and b.
First we can solve the equation a + b = 8 for a to get a = 8 - b.
Substitute this expression for a into the equation 2a - b = 7:
2(8 - b) - b = 7
Simplify the equation:
16 - 2b - b = 7
-3b = -9
b = 3
Substitute the value of b back into the equation a = 8 - b:
a = 8 - 3 = 5
Therefore, the values of a and b that satisfy the equation v = au bw are a = 5 and b = 3.