## Elementary Linear Algebra 7th Edition

the equation of the plane is $$7x+13y-z=0.$$
The equation of the plane is given by $$\left|\begin{array}{rrr}{x} & {y} & {z}&{1} \\ {0} & {0} & {0}&{1}\\{2} & {-1} & {1}&{1} \\{-3}&{2}&{5}&{1}\end{array}\right|= 0.$$ So, we have $$\left|\begin{array}{rrr}{x} & {y} & {z}&{1} \\ {0} & {0} & {0}&{1}\\ {2} & {-1} & {1}&{1} \\{-3}&{2}&{5}&{1}\end{array}\right|= \left|\begin{array}{rrr}{x} & {y} & {z} \\ {2} & {-1} & {1} \\{-3}&{2}&{5} \end{array}\right|=x(-5-2)-y(10+3)+z(4-3)=-7x-13y+z=0.$$ Hence, the equation of the plane is $$7x+13y-z=0.$$