The vectors v = [3, -4, -13], u = [-2, 0, 18 + k], and w = [-3, 0, 9]. are linearly independent if and only if k ? .
Added by Jesus B.
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First, we need to find the determinant of the matrix formed by the three vectors: | 3 2 3 | |-4 1 8 | |-13 18 k| We can expand this determinant along the first row: 3 | 1 8 | -4 | 18 k | -13 | 2 3 | = 3(1(3)-8(2)) - (-4)(18(3)-8(-13)) + (-13)(2(18)-3(-4)) = -48 Show more…
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