Question

Solve the following pair of equations for the vectors u and v. Assume i = (1,0) and j = (0;1). 7u + 6v = i,u - v = j u = i + j (Simplify your answers. Type integers or fractions.)

Answer 1

To solve the system of equations, use the method of substitution. Isolate u in the equation 7u + 6v = i and substitute the value into the second equation u - v = j. Solve the resulting system of equations to find the values of u and v.

Step-by-step explanation:

To solve the system of equations, we can use the method of substitution. From the equation 7u + 6v = i, we can isolate u:

7u = i - 6v
u = (i - 6v)/7
u = (1,0) - 6v/7

Substituting this value of u into the equation u - v = j:

(i - 6v)/7 - v = (0,1)

Simplifying this equation:

i - 6v - 7v = 7(0,1)
i - 13v = (0,7)

Now we have a system of linear equations with variables v. Solving this system will give us the value of v. Substituting the value of v into the equation u = (i - 6v)/7 will give us the value of u.