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Math54PracticeMT1 (Teleman)

# Math54PracticeMT1 (Teleman) - SAMPLE MIDTERM I MATH 54...

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SAMPLE MIDTERM I MATH 54 SEC.1, FALL 2009 80 POINTS, 80 MINUTES Question 1, 9 pts True or false? No justiFcation necessary. Correct answers carry 1 . 5 points, incorrect answers carry 1 . 5 points penalty. However, you will not receive a negative total score. T ± If x R 2 is not the zero vector, then each of its entries is non-zero. T ± The homogeneous system A x = 0 has a non-trivial solution if and only if it has at least one free variable. T ± If the equation A x = 0 admits the trivial solution, then the columns of the matrix A are linearly independent. T ± The collection { [1 , 2] T , [2 , 3] T , [3 , 4] T } is linearly independent. T ± In a linearly dependent collection of three vectors, each vector must be a linear combination of the other two. T ± The column space of the matrix A is the set of all vectors which can be written as A x , for some vector x . Question 2, 9 pts True or false? No justiFcation necessary. Correct answers carry 1 . 5 points, incorrect answers carry 1 . 5 points penalty. However, you will not receive a negative total score.

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Math54PracticeMT1 (Teleman) - SAMPLE MIDTERM I MATH 54...

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