Give the solution to the system that is represented by
1 0 2 5
0 1 1 3
0 0 0 0
i keep getting x=2z+5, z=-y+3 but don't know where to go from there. Thanks

Question

Give the solution to the system that is represented by 
1   0   2   5
0   1   1   3
0   0   0   0
i keep getting x=2z+5, z=-y+3 but don't know where to go from there. Thanks

anonymous · Answer

Don´t understand the signs you put. Can explain, please?

anonymous · Answer

so my teacher gave me a matrices and when it is a infinite # of solutions he wants us to write it out like (heres an example) -10Z+5, 5z-1,z)

anonymous · Answer

Well, the columns are x, y, z and the independet term, aren´t they? So I´ll write the next:  x+ 2z = 5; y+z = 3. And the answer would be x in terms of y and z. Do you think so?

anonymous · Answer

im not sure. Im reviewing for my exam and have been stuck on this one for a while and cannot find an example or anything. Thank you for your help though

anonymous · Answer

jkd is htis an augmented matrice

anonymous · Answer

yes

anonymous · Answer

x+2z=5

y+z=3

or

$$C_1+2C_3=5$$
$$C_2+C_3=3$$

you can see that both hae c_3 in each ... let us create parameters where t is our independent variable t.

anonymous · Answer

if 

$$c_3=t$$
$$c_1=5-2t$$
$$c_2=3-t$$

anonymous · Answer

now t can be any number that is why there is infinite solutions

anonymous · Answer

do you need this in vector forms?

anonymous · Answer

your

$$y=(5,3,0)^{T}+t(-2,-1,1)^T$$

anonymous · Answer

thank you for your help i think i got it!