Question

Find two basic solutions to the following system of homogeneous equations. left{egin{array}{r} x-y-2 z-w=0 \ 4 x+2 y+z-w=0 end{array} ight. Remark. Basic solutions can be obtained from a general solution of the form left[egin{array}{c} x \ y \ z \ w end{array} ight]=left[egin{array}{l} * s+* t \ * s+* t \ * s+* t \ * s+* t end{array} ight]=sleft[egin{array}{c} * \ * \ * \ * end{array} ight]+tleft[egin{array}{l} * \ * \ * \ * end{array} ight] by setting s = 1, t = 0 and s = 0, t = 1; see also Examples 1.38 and 1.39 of our text book.

          Find two basic solutions to the following system of homogeneous equations.

left{egin{array}{r}
x-y-2 z-w=0 \
4 x+2 y+z-w=0
end{array}
ight.

Remark. Basic solutions can be obtained from a general solution of the form

left[egin{array}{c}
x \
y \
z \
w
end{array}
ight]=left[egin{array}{l}
* s+* t \
* s+* t \
* s+* t \
* s+* t
end{array}
ight]=sleft[egin{array}{c}
* \
* \
* \
*
end{array}
ight]+tleft[egin{array}{l}
* \
* \
* \
*
end{array}
ight]

by setting s = 1, t = 0 and s = 0, t = 1; see also Examples 1.38 and 1.39 of our text book.

Find two basic solutions to the following system of homogeneous equations.

lefteginarrayr
x-y-2 z-w=0 4 x+2 y+z-w=0
endarray
ight.

Remark. Basic solutions can be obtained from a general solution of the form

left[eginarrayc
x y z w
endarray
ight]=left[eginarrayl
* s+* t * s+* t * s+* t * s+* t
endarray
ight]=sleft[eginarrayc
* * * *
endarray
ight]+tleft[eginarrayl
* * * *
endarray
ight]

by setting s = 1, t = 0 and s = 0, t = 1; see also Examples 1.38 and 1.39 of our text book.

Added by Dhruv V.

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