Homework: Module 02 Personalized Homework (4.1-4.2) Save Score: 0 of 1 pt 21 of

Question

Homework: Module 02 Personalized Homework (4.1-4.2) Save Score: 0 of 1 pt 21 of 22 (18 complete) HW Score: 62.88%, 13.83 of 22 pts 4.2.75 Question Help Solve using augmented matrix methods. 3x4x211 4x1 - x2= 2 O A. The unique solution is d(Simplity your answers.) O B. The system has infinitely many solutions. The solution is xand xt ? C. There is no solution. Click to select and enter your answer(s) and then click Check Answer. All parts showing (Simplify your answer. Type an expression using t as the variable.) Clear All Check Answer 2 11:14 2018-06-10

Explanation / Answer

1. The augmented matrix of the given linear system is A =

3

4

11

4

-1

2

To solve the given linear system, we will reduce A to its RREF as under:

Multiply the 1st row by 1/3

Add -4 times the 1st row to the 2nd row

Multiply the 2nd row by -3/19

Add -4/3 times the 2nd row to the 1st row

Then the RREF of A is

1

0

1

0

1

2

This implies that x1 = 1 and x2 = 2 which is the unique solution to the given linear system. Option A.

2. The augmented matrix of the given linear system is A =

3

6

6

-2

-4

-4

To solve the given linear system, we will reduce A to its RREF as under:

Multiply the 1st row by 1/3

Add 2 times the 1st row to the 2nd row

Then the RREF of A is

1

2

2

0

0

0

Thus, the given linear system is equivalent to x1+2x2 = 2 or, x1 =2-2x2. If x2 = t, then x1 = 2-2t, where t is an arbitrary real number. Thus, there are infinite solutions.Option B.

3

4

11

4

-1

2

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

---

---

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