IF X=2/3,Y=5/-2 AND Z=-4/13 FIND THE SCALARS P AND Q SUCH THAT PX + QY=Z
I WANT AN URGENT ANSWER PLEASE
(2/3) p - (5/2)q = -4/13
times 6
4 p - 15 q = - 24/13
times 13
52 p - 195 q = -24
It is hard to find two unknowns with one equation. What else do you know?
so pick any value for p, and figure a matching q!
suppose p = 35/41
then q = 2804/7995
(There are no integers p and q which will work)
To find the scalars P and Q such that PX + QY = Z, we need to substitute the given values of X, Y, and Z into the equation.
Substituting the given values:
P(2/3) + Q(5/-2) = -4/13
Let's simplify the equation step by step.
First, multiply P by (2/3):
(2/3)P + Q(5/-2) = -4/13
Now, multiply Q by (5/-2):
(2/3)P + (5/-2)Q = -4/13
To eliminate the denominators, we can multiply both sides of the equation by the least common multiple (LCM) of the denominators. The LCM of 3, 2, and 13 is 78.
Multiplying each term by 78:
78 * (2/3)P + 78 * (5/-2)Q = 78 * (-4/13)
This simplifies to:
52P - 195Q = -24
Therefore, by comparing coefficients, we can conclude that P = -24 and Q = 78.