4. Express the vector z = (-9,-7,-15) as linear combinations of u = (2, 1, 4), v = (1,-1, 3), and w = (3, 2, 5). 5. Show if these vectors are linearly independent or are linearly dependent in R^3. (-3, 0, 4), (5,-1, 2), (1, 1, 3)
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We can write this as a system of linear equations: -9 = 2a + b + 3c -7 = a - b + 2c -15 = 4a + 3b + 5c We can solve this system using Gaussian elimination or any other method. The solution is a = 1, b = -2, and c = 1. So, z = 1*u - 2*v + 1*w = (2,1,4) - Show more…
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