Solve the following problems, showing any necessary work. This includes row oper

Question

Solve the following problems, showing any necessary work. This includes row operations. How many solutions does each of the following systems of linear equations have? Circle the entries which led you to your conclusion: If there are no solutions, circle the row that indicates that there are no solutions. If there is exactly one solution, circle the pivots. If there is more than one solution, circle the columns which do not have pivots in them. [1 3 -3 -3 -2 0 1 -2 -1 0 0 0 1 3 1 0 0 0 1 -3 0 0 0 0 1|2 0 -3 3 -2] [1 -3 0 0 1 -1 0 0 0|1 3 2] [1 -2 -1 1 0 1 1 3 0 0 1 0 0 0 0 0|2 6 1 0]

Explanation / Answer

a) The system of linear equation have exactly one solution. From 5th row we have a x5 = -2 and using the back substitution we can find the rest. The pivot is 1 in the 5th row. Therefore system has exactly one solution.

b) From the third row we can see that 0=2 which is false. Therefore the system has no solution.

c) From the 4th row we have 0=0 which is true and hence system has more than one solutions.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.