Science:Math Exam Resources/Courses/MATH221/April 2009/Question 12 (g)
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Question 12 (g) 

If an matrix A is not invertible, then the columns of A must be linearly dependent. 
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Hint 

Science:Math Exam Resources/Courses/MATH221/April 2009/Question 12 (g)/Hint 1 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. The answer is true. If A is not invertible, then A has a nontrivial nullspace, i.e. there is a nonzero vector v such that Av = 0. This precisely means that the columns of A are linearly dependent. 