How do you write the augmented matrix for the system of linear equations #7x-5y+z=13, 19x=8z=10#?

1 Answer
Feb 20, 2017

Answer:

See explanation

Explanation:

Given:

#7x-5y+z=13" "............Equation(1)#
#19x=8z=10 " "................Equation(2)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Equation 2 can be 'split' into two equations

#7x-5y+z=13" "............Equation(1)#
#19xcolor(white)(-5y+z)=10 ...............Equation(2_a)#
#color(white)(7x-5y)+8z=10 ...............Equation(2_b)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Now this is how we write the augmented matrix

#[(7,-5,1,|,13),(19,0,0,|,10),(0,0,8,|,10)]#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("However; if you meant, how do we solve this. It is as follows")#

#[(7,-5,1,|,13),(19,0,0,|,10),(0,0,8,|,10)]#
#R_3-:8 and R_2-:19#
#" " darr #

#[(7,-5,1,|,13),(1,0,0,|,10/19),(0,0,1,|,10/8)]#
#R_1-7R_2#
#" " darr #

#[(0,-5,1,|,237/19),(1,0,0,|,10/19),(0,0,1,|,10/8)]#
#R_1-:(-5)#
#" " darr #

#[(0,1,-1/5,|,-237/95),(1,0,0,|,10/19),(0,0,1,|,10/8)]#
#R_1+1/5R_3#
#" " darr #

#[(0,1,0,|,-667/380),(1,0,0,|,10/19),(0,0,1,|,10/8)]#

#[ (1,0,0,|,10/19),(0,1,0,|,-667/380) ,(0,0,1,|,5/4)]#

You will need to check this. It is very easy to go wrong!