Determine the numbers a,b if the law of composition x*y=xy+2ax+by is commutative.
- print Print
- list Cite
Expert Answers
calendarEducator since 2010
write12,544 answers
starTop subjects are Math, Science, and Business
We have to determine a and b given that for x*y = xy + 2ax + by, the * operator is commutative.
x*y = y*x
=> xy + 2ax + by = yx + 2ay + bx
=> 2ax + by = 2ay + bx
equating the coefficients of x and y we get
2a = b
If the numbers a and b are related as 2a = b, then * is commutative
Related Questions
- Given the law of composition x*y= xy+4mx+2ny, determine m and n if the law is commutative.
- 1 Educator Answer
- Solve for x and y x^3-y^3=7 x^2+xy+y^2=7
- 2 Educator Answers
- Given y=3x/(x^2-9) determine the numbers m and n if y=m/(x-3)+n/(x+3)
- 1 Educator Answer
- What are x and y if 4^(x/y)*4^(y/x)=32 and log 3 (x-y)=1-log 3 (x+y) ?
- 2 Educator Answers
- What are x,y and z? x+y=-3 x+z=-2 xy+yz+xz=2
- 1 Educator Answer
If a law of composition is commutative, that means that x*y = y*x, for any value of x and y.
We'll substitute x*y and y*x by the given expression:
x*y = xy + 2ax + by (1)
y*x = yx + 2ay + bx (2)
We'll put (1) = (2) and we'll get:
xy + 2ax + by = yx + 2ay + bx
We'll remove like terms:
2ax + by = 2ay + bx
We'll move the terms in a to the left side and the terms in b to the right side:
2ax - 2ay = bx - by
We'll factorize and we'll get:
2a(x-y) = b(x-y)
We'll divide by x - y:
2a = b
a = b/2
So, for the law to be commutative, we find a = b/2, for any value of a and b.
Unlock This Answer Now
Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.
Student Answers