Full working is greatly appreciated, thank you! :)
In R4, with the Euclidean inner product, consider the vectors w1 = (2,5,4,1), w2 = (0.3.1.2), and w3 = (2, 2, 3, -1). Let W = span (w1, w2, w3). Let W be the orthogonal complement of W, Show that if and only if v . wj = 0 for j = 1, 2, 3. Find a basis for W .
Show transcribed image textIn R4, with the Euclidean inner product, consider the vectors w1 = (2,5,4,1), w2 = (0.3.1.2), and w3 = (2, 2, 3, -1). Let W = span (w1, w2, w3). Let W be the orthogonal complement of W, Show that if and only if v . wj = 0 for j = 1, 2, 3. Find a basis for W .