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samplefinal

# samplefinal - SAMPLE FINAL EXAM MATH 54 SEC.1 FALL 2009 90...

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SAMPLE FINAL EXAM MATH 54 SEC.1, FALL 2009 90 POINTS, 180 MINUTES Question 1, 18 pts True or false? No justification necessary. Correct answers carry 1 . 5 points, incorrect answers carry 1 . 5 points penalty. However, you will not receive a negative total score on any group of 6 questions. T F If an augmented matrix [ A b ] is transformed into [ C d ] by elementary row operations, then the systems a x = b and C x = d have exactly the same solution sets. T F If { u , v , w } is linearly independent, then u , v and w are not in R 2 . T F For any matrix A , det( - A ) = - det( A ). T F For any square matrix A , det( A T A ) 0. T F If u and v are in R 2 and det[ u v ] = 10, then the area of the triangle in the plane with vertices at 0 , u and v is 10. T F If two row exchanges are made in succession, then the new determinant equals the old determinant. T F If λ + 5 is a factor of the characteristic polynomial of A , then 5 is an eigenvalue of A . T F Eigenvalues of a matrix must be non-zero scalars. T F A square matrix A is invertible if and only if there is a coordinate system in which the linear transformation x

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