Consider a system of three linear equations in three variables. Give examples of two reduced forms that are not row-equivalent if the system is: a) onsistent and dependent. b) Inconsistent

djeljenike 2020-10-26 Answered
Consider a system of three linear equations in three variables. Give examples of two reduced forms that are not row-equivalent if the system is: a) onsistent and dependent. b) Inconsistent
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Asma Vang
Answered 2020-10-27 Author has 93 answers

Step 1 Answer for (a). Let us consider following two systems

(I) {x  z=0y =0x + y  z=0 and (II) {x  y=0y  z=0x  z=0

Notice that augmented systems of the above two systems are as follows (I) [101001001110] and (II) [110001101010]

Note that the reduced forms the above two systems are

(I) [101001000000] and (II) [101001100000]

Therefore reduced forms of the systems (I) and (II) are not row-equivalent. Notice that both systems are consistent and dependent because solutions to the systems are Solution set of (I) : {(t, 0, t)| t R}
Solution set of (II) : {(t, t, t)| t R}

Step 2 Answer for (b). Let us consider following two systems (I) {x  z=0y =0x + y  z=1 and (II) {x  y=0y  z=0x  z=1

Notice that augmented systems of the above two systems are as follows (I) [101001001111] and (II) [110001101011]

Note that the reduced forms the above two systems are (I) [101001000001] and (II) [101001100001] Therefore reduced forms of the systems (I) and (II) are not row-equivalent. Further note that both the systems are inconsistent because from last row of reduced from we see that 0=1, which is not possible.

Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-06-01

Find the linear approximation of the function f(x)=4x at a=0
Use L(x) to approximate the numbers 3.9 and 3.99 Round to four decimal places

asked 2021-02-01
Write the general forms of the equations of the lines that pass through the point and are (a) parallel to the given line and (b) perpendicular to the given line. Point (−1, 0) Line y=-3
asked 2020-11-30
Use Cramer’s Rule to solve (if possible) the system of linear equations.
2x-y=-10
3x+2y=-1
asked 2022-02-25
If we were given two points on a linear equation (x1,y1),(x2,y2), it is quite easy to find the slope and use substitution to find the slope intercept form y=mx+b, to graph it.
Is it possible to solve for b strictly in terms of x1,y1,x2,y2?
asked 2021-02-11
What is a system of linear equations? Provide an example with your description.
asked 2021-03-05
Use cramers
asked 2022-06-16
| 1 2 5 4 5 8 3 3 3 | | x 1 x 2 x 3 | = | b 1 b 2 b 3 |
I need to determine the values of the b constants that would guarantee that the linear system is consistent. I tried to find the inverse of the matrix on the left hand side so that I could try and solve for the x variables and see if there are any values of b that would cause the system to be inconsistent but the matrix is singular. I then went on to put the matrix in reduced row echelon form.
| 1 0 3 0 1 4 0 0 0 |
From this I was able to derive the equations: x 1 3 x 3 = b 1 , x 2 4 x 3 = b 2 , and 0 = b 3 . I know that the answer is b 1 = b 2 + b 3 , but I don't know how to get that with the given information.