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Question

If [xy4z+6x+y]=[8w06], then find the values of x,y,z and w.

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Solution

Since, matrices are equal then, their corresponding elements are also equal.
xy=8 ---- ( 1 )
4=ω ---- ( 2 )
z+6=0 ----- ( 3 )
x+y=6 ------ ( 4 )
From equation ( 1 ),
xy=8
x=8y ---- ( 5 )
Substituting x=8y in equation ( 4 ),
8y+y=6
8+y2y=6
8+y2=6y
y26y+8=0
(y4)(y2)=0
y=4 and y=2
Substituting value of y in equation ( 5 ),
If y=4
x=84
x=2
If y=2
x=82
x=4
From equation ( 3 ),
z+6=0
z=6
x=2 or x=4, y=4 or y=2, ω=4 and z=6

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