u = (9, 2)
v = (-5, -2)
2u - 3v = ?
To find 2u - 3v, we multiply each component of u by 2 and each component of v by 3, and then subtract the corresponding components.
2u = 2(9, 2) = (18, 4)
3v = 3(-5, -2) = (-15, -6)
Now, subtract the corresponding components:
2u - 3v = (18, 4) - (-15, -6) = (18 + 15, 4 + 6) = (33, 10)
Therefore, 2u - 3v = (33, 10).
To find the expression 2u - 3v, we multiply each component of u and v by the corresponding coefficients and then subtract the results.
Given:
u = (9, 2)
v = (-5, -2)
Coefficients:
a = 2
b = -3
Now, let's calculate 2u - 3v step-by-step:
1. Multiply each component of u by the coefficient a:
2u = 2 * (9, 2)
2u= (2 * 9, 2 * 2)
2u = (18, 4)
2. Multiply each component of v by the coefficient b:
3v = -3 * (-5, -2)
3v = (-3 * -5, -3 * -2)
3v = (15, 6)
3. Subtract the results:
2u - 3v = (18, 4) - (15, 6)
2u - 3v = (18 - 15, 4 - 6)
2u - 3v = (3, -2)
Therefore, 2u - 3v = (3, -2).