# Span 1 4 4 3 1 1 b 0 0 1 span 1 4 4 3 1 1 c 1 c 2 1 4

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span , 1 4 4 3 1 1 b = 0 0 1 span , , 1 4 4 3 1 1 c 1 + c 2 = 1 4 4 3 1 1 0 0 1
10. –/2 pointsHoltLinAlg1 2.2.040. Find all values of h such that the vectors span where Solution or Explanation since when the vectors and are parallel and do not span 11. –/2 pointsHoltLinAlg1 2.2.042. Find all values of h such that the vectors span where { a 1 , a 2 , a 3 } R 3 a 1 = , a 2 = , a 3 = 1 h 7 4 2 5 1 2 2 h (No Response) h 16 . { a 1 , a 2 } R 2 , a 1 = , a 2 = . 2 h 3 5 h (No Response) h , 10 3 h = 10 3 2 10 3 3 5 R 2 . , . = 2
12. –/1 pointsHoltLinAlg1 2.2.052. Determine if the statement is true or false, and justify your answer. If a set of vectors includes 0 , then it cannot span R n . False, a set of vectors cannot span R n unless it includes the zero vector. True, since any linear combination involving the zero vector will be the zero vector. False, the zero vector can be included with any set of vectors which already span R n True, since a set of vectors which includes the zero vector can only span R n 1 at most. R n . .
13. –/1 pointsHoltLinAlg1 2.2.053. Determine if the statement is true or false, and justify your answer. Suppose A is a matrix with n rows and m columns. If then the columns of A span R n . . ,
14. –/1 pointsHoltLinAlg1 2.2.054. Determine if the statement is true or false. Suppose A is a matrix with n rows and m columns. If then the columns of A span R n . Solution or Explanation False, by Example 5. 15. –/1 pointsHoltLinAlg1 2.2.055. Determine if the statement is true or false, and justify your answer. If A is a matrix with columns that span R n , then has nontrivial solutions. A x = False. Consider A = [1]. True. For A x = 0 to have no nontrivial solutions, the columns of A could not span R , 0 n . .