2Q1920 MATH149 OLSW.docx - 2 nd Quarter 2019-2020 149-1...

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Math 149-1 2 nd Quarter, 2019 -2020 ONLINE SEATWORK 1 I. Respond with TRUE or FALSE to each of the following assertions. No erasures. (2 pts) 1. A consistent, independent system has only one solution. TRUE 2. A homogeneous linear system has only the trivial solutions if all the unknowns are all zero. TRUE 3. A homogeneous linear system with more unknowns than equations have infinitely many solutions. TRUE 4. The graphs of a linear system in three variables are three lines. FALSE 5. The solution set of a consistent, dependent system is represented by parameter/s. TRUE 6. A matrix is in reduced row echelon form if every leading coefficient is 1 and is the only nonzero entry in its column. TRUE 7. If two rows of a determinant are interchanged, the value of the resulting determinant is the negative of the given determinant . TRUE 8. All square matrices have inverses. FALSE 9. The determinant of a triangular matrix is the product of the entries on its main diagonal. TRUE 10. The determinants of a matrix and its transpose are equal. TRUE
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Unformatted text preview: II . Perform as indicated. 11 . Find PQ +PR if P = [ 2 2 3 3 − 1 2 ] , Q = [ 1 2 2 3 1 ] , R = [ − 1 2 1 2 − 2 ] . ( 10 pts.) 1 Math 149-1 2 nd Quarter, 2019 -2020 ONLINE SEATWORK 1 1 2. Solve the homogeneous linear system 3 x − 5 y + 3 z = 2 x − 3 y + 4 z = 7 x − 11 y + 11 z = . (15 pts.) 2 Math 149-1 2 nd Quarter, 2019 -2020 ONLINE SEATWORK 1 3 Math 149-1 2 nd Quarter, 2019 -2020 ONLINE SEATWORK 1 13. Solve the system by Matrix Inversion 3 x + 4 y − z =− 7 x − 5 y + 2 z = 19 5 x + y − 2 z = 5 ¿ } ¿ } ¿ ¿¿ . (20 pts.) 4 Math 149-1 2 nd Quarter, 2019 -2020 ONLINE SEATWORK 1 14. Use Gaussian Elimination to solve the system 2 x − 5 y + 3 z =− 18 3 x + 2 y − z =− 12 x − 3 y − 4 z =− 4 ¿ } ¿ } ¿ ¿¿ . (20 pts.) 5 Math 149-1 2 nd Quarter, 2019 -2020 ONLINE SEATWORK 1 15. Evaluate [ 4 − 4 2 1 1 2 3 2 3 4 3 2 1 ] by a) cofactor expansion using row 2. 6 Math 149-1 2 nd Quarter, 2019 -2020 ONLINE SEATWORK 1 b) row reduction (15 pts.) 7...
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