If #A=((3,2), (-3,-4))# and #B=((0,-5),(-2,1))#, What are the matrices X and Y such that 2A -3X = B and 3A+2Y = 2B?

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1 Answer
Shwetank Mauria
Jan 18, 2018

#X=((2,3),(-4/3,-3))# and #Y=((-9/2,-8),(5/2,7))#

Explanation:

As #2A-3X=B#, #3X=2A-B# and

#X=1/3(2A-B)#

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

= #1/3((2xx3-0,2xx2-(-5)),(2xx(-3)-(-2),2xx(-4)-1))#

= #1/3((6,9),(-4,-9))#

= #((2,3),(-4/3,-3))#

and as #3A+2Y=2B#, #2Y=2B-3A#

and #Y=1/2(2B-3A)#

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

= #1/2((2xx0-3xx3,2xx(-5)-3xx2),(2xx(-2)-3xx(-3),2xx1-3xx(-4)))#

= #1/2((-9,-16),(5,14))#

= #((-9/2,-8),(5/2,7))#

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