If given A,B,C, Find constants x,y |xA +yB=C

In summary, the question asks for constants x and y such that the sum of vectors A and B multiplied by x and y respectively is equal to vector C. The attempt at a solution involves finding the total vector for each given vector and setting up a system of equations to solve for x and y.
  • #1
astroman707
61
5

Homework Statement


Three vectors are given:
A=2i+3j, B=1i+5j, C=-1i+3j
Find constants x and y such that xA+yB=C

Homework Equations


N/A

The Attempt at a Solution


The form of the final equation reminded me if standard form of a slope, so I found the total vector for A,B, and C. I was then going to put it in the form Ax+By=C, but then I realized I’d be solving for slope, and I don’t think that’s the direction I want to go.
 
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  • #2
try separating the vector equation xA + yB into their two components - that is two equations, one for i and one for j
 

FAQ: If given A,B,C, Find constants x,y |xA +yB=C

1. What does the equation "xA + yB = C" mean?

The equation "xA + yB = C" represents a linear combination of two variables, A and B, to form a constant, C. This means that for any given values of A and B, there exists a unique pair of constants, x and y, that when multiplied by A and B and added together, will equal C.

2. How do I solve for the constants x and y?

To solve for x and y, you need to have at least two equations with the same variables. This means that you need to have two different combinations of A and B that equal two different values of C. Once you have these two equations, you can use algebraic methods such as substitution or elimination to solve for x and y.

3. Can there be more than one solution for x and y?

Yes, there can be infinitely many solutions for x and y that satisfy the equation "xA + yB = C". This is because there are infinite combinations of x and y that can be multiplied by A and B to equal C. However, if you have two equations with the same variables, there will typically be one unique solution for x and y.

4. What if the values of A and B are unknown?

If the values of A and B are unknown, then you will need to have additional information or equations in order to solve for x and y. Without knowing the values of A and B, you cannot determine unique values for x and y.

5. How is this equation used in scientific research?

The equation "xA + yB = C" can be used in a variety of scientific research fields, such as chemistry, physics, and engineering. It can be used to model or predict relationships between different variables, and can also be used to solve for unknown values or constants in experiments. Additionally, this equation can be used to analyze complex data sets and determine patterns or correlations between variables.

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