linear algebra: Find a, b, c so system has 0,1,more solns

[dsuarez3]

can someone help I don't know how to tackle to questions

1. find if possible conditions on a, b, and c such that the system of linear equations has a. no solution, b. exactly one solution and c. infinite number of solutions

2x-1y+z =a
1x+1y+2z=b
+3y+3z=c

2. This question I was not able to figure out
homogenous system of linear

the exponent to this problem is in the bottom

2X1 + 4x2 -7X3 =0
1x1 - 3x2+ 9x3=0
6x1 + 9x3=0

3. the last question
I tried to solve this question but K =0

It said:
Determine the values of K such that the system of linear equations has exactly one solution.

1x-1y+2z=0
-1x+1y-1z=0
1x+ky+1z=0

 

[Deleted member 4993]

Re: linear algebra, help

can someone help I don't know how to tackle to questions

1. find if possible conditions on a, b, and c such that the system of linear equations has a. no solution, b. exactly one solution and c. infinite number of solutions

2x-1y+z =a
1x+1y+2z=b
+3y+3z=c


2. This question I was not able to figure out
homogenous system of linear

the exponent to this problem is in the bottom

\(\displaystyle 2x_1 + 4x_2 - 7x_3 =0\)
\(\displaystyle 1x_1 - 3x_2 + 9x_3 =0\)
\(\displaystyle 6x_1 + 0x_2 + 9x_3 =0\)

3. the last question
I tried to solve this question but K =0

It said:
Determine the values of K such that the system of linear equations has exactly one solution.

1x-1y+2z=0
-1x+1y-1z=0
1x+ky+1z=0

What is the condition for a homogeneous system to have "unique" solition?

Please show us your work - and exactly where you are stuck. That will help us determine where to start to help you.

 

[stapel]

1. find if possible conditions on a, b, and c such that the system of linear equations has a. no solution, b. exactly one solution and c. infinite number of solutions

2x-1y+z =a
1x+1y+2z=b
+3y+3z=c

Solve the system for x, y, and z in terms of a, b, and c. Then use what you've learned about solutions and system types to pick values for a, b, and c that give you the desires numbers of solutions.

a) If a system has no solutions, what sort of solution do you get in the end? In particular, what sort of rows tell you that the system has no solution?

b) For a system to have one solution, you must have specific numerical values for each of x, y, and z. What must you do with a, b, and c to make that happen?

c) For a system to have infinitely-many solutions, what sort of solution must you have in the end? (Think about the weird parametrized solutions you've gotten, with answers like (x, y, z) = (t, 3t + 4, 6 - t).)

2. This question I was not able to figure out
homogenous system of linear
the exponent to this problem is in the bottom

I'm sorry, but I don't know what this means. To what "exponent" are you making reference?

2X1 + 4x2 -7X3 =0
1x1 - 3x2+ 9x3=0
6x1 + 9x3=0

This system has five variables, X₁, x₁, x₂, X₃, and x₃, and only three equations. It cannot then have a unique solution. Was that what you meant?

3. the last question I tried to solve this question but K =0

It said: Determine the values of K such that the system of linear equations has exactly one solution.

1x-1y+2z=0
-1x+1y-1z=0
1x+ky+1z=0

Please reply showing what you tried, clarifying what you mean by "But K = 0". Also, please provide the relationship, if any, between the variables K and k.

Thank you!

Eliz.

 

[dsuarez3]

linear algebra, help

I can not figure homogenous

 

[stapel]

I can not figure homogenous

The process for solving linear systems is the same for homogenous and non-homogenous systems. Just use the same method(s) you've always used! :wink:

Eliz.