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14 February, 16:48

Find values a and b that satisfy a∙〈5,-4,0〉+b∙〈2,2,-3〉=〈11,-16,-6〉.

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  1. 14 February, 17:14
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    Therefore a = 5 and b = 2

    Step-by-step explanation:

    Given,

    a (5,-4,0) + b (2,2,-3) = (11,-16,-6)

    ⇔ (5a,-4a, 0) + (2b, 2b,-3b) = (11,-16,-6)

    ⇔ (5a+2b,-4a+2b,-3b) = (11,-16,-6)

    Therefore

    5a+2b = 11 ... (1) - 4a+2b=-16 ... (2) - 3b=-6 ... (3)

    From equation (3) we get

    -3b = - 6

    ⇔b = 2

    Putting the value of b in equation (2)

    -4a + 2.2 = 16

    ⇔-4a = - 16-4

    ⇔ a = 5

    Therefore a = 5 and b = 2
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