67. Consider linearly independent vectors v1, v2, ..., vp a subspace V of R" and vectors w1, w2, ..., ūwg that span V. Show that there is a basis of V that consists of all the v; and some of the w j. Hint: Find a basis of the image of the matrix in | A = | 01 W1 p .. .. | | 68. Use Exercise 67 to construct a basis of R* that consists of the vectors 1. [1' 4 3 4 8. and some of the vectors ē1, ė2, é3, and ē4 in R“.

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