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Unformatted text preview: v 1 , v 2 , . . . , v p is LI if and only if the vector equation x 1 v 1 + x 2 v 2 + + x p v p = has ONLY the trivial solution. EXAMPLE. Are the vectors 1-3 2 , 2-5 3 , and 4 1 linearly independent? Justify your answer. Any list of vectors containing the zero vector is LD. Why? Any list of vectors with more vectors than rows is LD. Why? If one vector in a list is a multiple of another vector in the list, then the list is LD. Why? How many pivot columns must a 9 6 matrix have if its columns are linearly independent? Why? HOMEWORK: SECTION 1.7...
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