What conditions must b1, b2, and b3 satisfy so linear system is consistent?

[Helpmee]

I have an homework problem and need help. Here it comes:
What conditions must b1,b2 and b3 satisfy in order for the system of equations
x1+2x2+3x3=b1
2x1+5x2+3x3=b2
x1+8x3=b3
to be consisten? (We need to solve this question using matrix form.)

 

[Deleted member 4993]

I have an homework problem and need help. Here it comes:
What conditions must b1,b2 and b3 satisfy in order for the system of equations
x1+2x2+3x3=b1
2x1+5x2+3x3=b2
x1+8x3=b3
to be consisten? (We need to solve this question using matrix form.)

What would be the matrix representation of the above set of simultaneous equations

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

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[stapel]

I have an homework problem and need help. Here it comes:

What conditions must a, b, and c satisfy in order for the following system of equations to be consistent?

. . . . .1x + 2y + 3z = a
. . . . .2x + 5y + 3z = b
. . . . .1x + 0y + 8z = c

(We need to solve this question using matrix form.)

(I've renamed the variables so we don't have to bother with typing subscripts here. The methods and results remain the same.)

What result do you get when a matrix displays a "consistent" result? In particular, what format(s) should you not get (as this/these result(s) would mean that the system is "indeterminate" or "inconsistent")? If you apply row operations to the matrix (or plug into technology, such as a graphing calculator) to solve the matrix, what results to you get on the right-hand side (that is, the "answer" column)? Where might this lead?

Please reply showing your thoughts and reasoning so far. Thank you!

 

[Ishuda]

I have an homework problem and need help. Here it comes:
What conditions must b1,b2 and b3 satisfy in order for the system of equations
x1+2x2+3x3=b1
2x1+5x2+3x3=b2
x1+8x3=b3
to be consisten? (We need to solve this question using matrix form.)

Compute the determinate of the system [given by stapel above], see
http://www.purplemath.com/modules/determs2.htm
for example. If it is not zero, the matrix has an inverse and any a, b, and c [to again use stapel's post] is allowable.