How to find the final form of augmented matrix when solving for the inverse of this system of equations? #2x+3y=4# #4x+5y=5#

A) #[(1,0),(0,1)]|[(5/2,-3/2),(-3,4)]#

B) #[(1,0),(0,1)]|[(-5/2,3/2),(2,-1)]#

C) #[(1,0),(0,1)]|[(5,-3),(-4,2)]#

D) #[(1,0),(0,1)]|[(5/2,-3/2),(-2,1)]#

I have zero clue of what the question wants me to do and I've never heard of finding the inverse of an augmented matrix.... Plz halp :/

1 Answer
Narad T.
Jul 30, 2018

The answer is #option (B)#

Explanation:

You have #2# equations with #2# unknowns

#{(2x+3y=4),(4y+5y=5):}#

The equations can be written as

#AX=B#

where #A# is a matrix

#((2,3),(4,5))((x),(y))=((4),(5))#

The solution is

#X=A^-1B#

Where #A^-1# is the inverse of matrix #A#

To calculate the inverse, proceed as follows,

Write side by side matrix #A# and the unit matrix #I#

Perform row operations until the unit matrix #I# is on the left and the inverse on the RHS

#((2,3),(4,5))|((1,0),(0,1))#

#R2larr( R2-2R1)#

#((2,3),(0,-1))|((1,0),(-2,1))#

#R2larr(R2*-1)#

#((2,3),(0,1))|((1,0),(2,-1))#

#R1larrR1-3R2#

#((2,0),(0,1))|((-5,3),(2,-1))#

#R1larr((R1)/2)#

#((1,0),(0,1))|((-5/2,3/2),(2,-1))#

The answer is #option (B)#

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