Let u = (5, 6, 4). v = (4, - 1, - 6). w = (22, 9, h - 2). Find a value for h so

Question

Let u = (5, 6, 4). v = (4, - 1, - 6). w = (22, 9, h - 2). Find a value for h so that W is in the span of the vectors u and v. The value of h is Find a value for h so that u is in the span of the vectors v and w. The value of h is If h is the value from, is the set {u, v, w} linearly independent?

Explanation / Answer

(a) 5a + 4b = 22, 6a-b = 9 ==> 5a + 4b = 22, 24a-4b = 36 ==> 29a = 58 ==> a = 2, b = 3 2(4) + 3(-6) = h - 2 ==> h = -8 (b) 4a + 22b = 5, -a + 9b = 6 ==> 4a + 22b = 5, -4a + 36b = 24 ==> 58b = 29 ==> b = 0.5, a = -1.5 4 = -1.5(-6) + 0.5(h-2) ==> 4 = 9 + 0.5h -1 ==> 0.5h = -4 ==> h = -8 NO, it is linearly dependent

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