# Algebra lineal sistemas de ecuaciones

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• Publicado : 23 de noviembre de 2010

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WeBWorK Tarea3 Sist Ecs, fecha de cierre : 10/25/2010 at 11:59pm CDT.  1. (1 pt) Solve the system   x + 2y= 8 −2y − z= −3  −x − 4z= 10 Give the coordinates of the solution below. x= y= z= 2. (1 pt) Solve the system using the substitution or elimination method 5x + 2y = −4 7x + 3y = −5 How many solutions are there to this system? • • • • • • A. None B. Exactly 1 C. Exactly 2 D. Exactly 3 E.Inﬁnitely many F. None of the above 

S1 2010-2011 f-algebra 1SM1
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How many solutions are there to this system? • A. None • B. Exactly 1 • C. Exactly 2 • D. Exactly 3 • E. Inﬁnitely many • F. None of the above

If there is one solution, give its coordinates in the answer spaces below. If there are inﬁnitely many solutions, enter z in the answer blank for z, enter a formula for y in termsof z in the answer blank for y and enter a formula for x in terms of z in the answer blank for x. If there are no solutions, leave the answer blanks for x, y and z empty. x= y= z= 4. (1 pt) Use the method of elimination to solve the system 2x − 4y 4x − y

If there is one solution, give its coordinates in the answer spaces below. If there are inﬁnitely many solutions, enter x in the answer blankfor x and enter a formula for y in terms of x in the answer blank for y. If there are no solutions, leave the answer blanks for x and y empty. x= y= 3. (1 pt) Solve the system by ﬁnding the reduced row-echelon form of the augmented matrix.   x + 2y + 4z = 5 x − y + 16z = 17  x + 12z = 13

= 2, = 11.

Your answer is If there is more than one point, type the points separated by a comma (i.e.:(1,2),(3,4)). If the system has no solutions, type none in the answer blank. 5. (1 pt) Solve the system using elimination   2x − 3y + 5z= 20 −5x − 6y − 4z= −38  3x − y − 2z= 5 How many solutions are there to this system? • A. None • B. Exactly 1 • C. Exactly 2 • D. Exactly 3 • E. Inﬁnitely many • F. None of the above
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reduced row-echelon form:

3.

If there is one solution, give itscoordinates in the answer spaces below. If there are inﬁnitely many solutions, enter z in the answer blank for z, enter a formula for y in terms of z in the answer blank for y and enter a formula for x in terms of z in the answer blank for x. If there are no solutions, leave the answer blanks for x, y and z empty. x= y= z= 6. (1 pt) Write the augmented matrix of the system   −9x−12y−22z=−84 −77y−4z= −4  −92x +38z=−48    

• • • • • • 4.

 1 1 0 0  0 1 0 4  −2 0 0 0 A. Unique solution: x = 1, y = 4, z = −2 B. No solutions C. Unique solution: x = 1, y = 4, z = 0 D. Inﬁnitely many solutions E. Unique solution: x = 1, y = 4 F. None of the above  0 1 0 0  0 1 0 2  −2 0 0 1 A. Inﬁnitely many solutions B. Unique solution: x = 0, y = 2 C. No solutions D. Unique solution: x = 2, y =−2 E. Unique solution: x = 0, y = 2, z = −2 F. None of the above 

• • • • • •

8. (1 pt) Solve the system using matrices (row operations) −4x − 3y= −10 x − 4y= 12 x= y=

7. (1 pt) The reduced row echelon form of a system of linear equations in x and y or in x, y and z is given. For each system, determine whether it has a unique solution (in this case, ﬁnd the solution), inﬁnitely manysolutions, or no solutions. 1.   0 1 0  0 1 0  0 0 0 • • • • • • 2.  1  0 0 • • • • • • 0 1 0 0 0 0  3 −1  0 A. Unique solution: x = 0, y = 0 B. Inﬁnitely many solutions C. Unique solution: x = 1, y = 1, z = 0 D. No solutions E. Unique solution: x = 0, y = 0, z = 0 F. None of the above

9. (1 pt) Solve the system using matrices (row operations)   2x − 3y + 3z = 0 5x − 6y + 2z = 16  6x+ y + 2z= −12 How many solutions are there to this system? • A. None • B. Exactly 1 • C. Exactly 2 • D. Exactly 3 • E. Inﬁnitely many • F. None of the above

A. Inﬁnitely many solutions B. Unique solution: x = −1, y = 3 C. Unique solution:x = 3, y = −1 D. No solutions E. Unique solution: x = 0, y = 0, z = 0 F. None of the above
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If there is one solution, give its coordinates in the...