Let u = (1, 1, 1), v = (-2, 2, 3), and b = (1, 3, 2). Is it possible to express b as a linear combination of u and v? That is, is b in the span {u, v} of u and v?
Added by Angela M.
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This can be rewritten as a system of linear equations: 1a - 2b = 1 1a + 2b = 3 1a + 3b = 2 We can solve this system using Gaussian elimination: 1 -2 1 | 1 1 2 3 | 3 1 3 2 | 2 R2 - R1 -> R2 0 4 2 | 2 R3 - R1 -> R3 0 5 1 | 1 R3 - 5R2/4 -> R3 0 0 -3/4 | Show more…
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