Find the Variables x[[2],[-3]]+y[[-4],[-2]]=[[-4],[-1]]

Problem

x*[[2],[−3]]+y*[[−4],[−2]]=[[−4],[−1]]

Solution

1. Distribute the scalars x and y into the vectors to create a system of linear equations.

[[2*x],[−3*x]]+[[−4*y],[−2*y]]=[[−4],[−1]]

2. Combine the vectors on the left side by adding their corresponding components.

[[2*x−4*y],[−3*x−2*y]]=[[−4],[−1]]

3. Set up the system of equations by equating the components of the vectors.

2*x−4*y=−4

−3*x−2*y=−1

4. Simplify the first equation by dividing all terms by 2

x−2*y=−2

5. Solve for x in the simplified first equation.

x=2*y−2

6. Substitute the expression for x into the second equation.

−3*(2*y−2)−2*y=−1

7. Distribute and solve for y

−6*y+6−2*y=−1

−8*y=−7

y=7/8

8. Substitute the value of y back into the expression for x

x=2*(7/8)−2

x=7/4−8/4

x=−1/4

Final Answer

x=−1/4,y=7/8

Want more problems? Check here!