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Math Help - Vectors: Finding coefficients to scalars with given vectors.

  1. #1
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    Vectors: Finding coefficients to scalars with given vectors.

    The problem gives three vectors: a=<4,3>, b=<4,-1>, and c=<6,2>.
    Using the equation c=sa+tb, with s and t as scalars, I'm supposed to find the exact values of s and t. However, I am clueless on how to solve this using a method that doesn't involve random guessing. The second scalar has thrown off my train of thought.

    Using what the problem has provided, I rewrote the equation to:
    <6,2> = s<4,3> + t<3,-1> and using the vector multiplication and addition properties I got:

    <6,2> = <4s + 3t, 3s - t> and that's where I got stumped. Am I on the right track or am I'm not doing this right?
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  2. #2
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    Yes, you're almost there.

    So now you have two equations in two unknowns:

    \displaystyle 4s + 3t = 6 and \displaystyle 3s - t = 2.

    Solve them simultaneously.
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  3. #3
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    Well I feel stupid for mixing up the numbers in my work with the given varibles, but thanks for showing how to finish the rest of the problem.
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