Given vectors m (-2 1) and n (2 4) find the coordinates of the vector and if a = 2m-3n.

In general, the coordinates of a vector can be written as follows:

X = (ax + bx);

Y = (ay + by);

Since it is necessary to determine the vector a = 2 * m – 3 * n, we get:

X = (2 * mx – 3 * nx);

Y = (2 * my -3 * ny).

Moreover, in the given example, the following coefficients:

mx = -2; nx = 2;

my = 1; ny = -4.

Therefore, the vector a = 2 * m – 3 * n = (2 * (-2) – 3 * 2; 2 * 1 – 3 * (-4)) = (-4 – 6; 2 + 12) = (- 10; 14)

Answer: the coordinates of the given vector a (-10; 14).