Exercises 1. Given the following set of vectors in P,: S, = {u, v, w} where u = 2+ x?, v = 3 – x and w = 5 – 2x + 4x². (i) Is it possible to express w as a linear combination of u & v? (ii) Is S,...

Exercises<br>1. Given the following set of vectors in P,:<br>S, = {u, v, w} where u = 2+ x?, v = 3 – x and w = 5 – 2x + 4x².<br>(i) Is it possible to express w as a linear combination of u & v?<br>(ii) Is S, linearly dependent or linearly independent?<br>2. Given the following set of vectors in R3:<br>S, = {u, v, w} where u = (1,2,3), v = (4,5,6) and w = (7,8,9).<br>%3D<br>(i) Is it possible to express v as a linear combination of u & w?<br>(ii) Is S, linearly dependent or linearly independent?<br>

Extracted text: Exercises 1. Given the following set of vectors in P,: S, = {u, v, w} where u = 2+ x?, v = 3 – x and w = 5 – 2x + 4x². (i) Is it possible to express w as a linear combination of u & v? (ii) Is S, linearly dependent or linearly independent? 2. Given the following set of vectors in R3: S, = {u, v, w} where u = (1,2,3), v = (4,5,6) and w = (7,8,9). %3D (i) Is it possible to express v as a linear combination of u & w? (ii) Is S, linearly dependent or linearly independent?

Jun 04, 2022

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Exercises 1. Given the following set of vectors in P,: S, = {u, v, w} where u = 2+ x?, v = 3 – x and w = 5 – 2x + 4x². (i) Is it possible to express w as a linear combination of u & v? (ii) Is S,...

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