Answer to Question #305187 in Linear Algebra for misfit

Question #305187

Determine the basis for the set of vectors lying on the plane π‘Š = {(π‘₯, 𝑦, 𝑧): 3π‘₯ + 𝑦 βˆ’ 5𝑧 = 0}


1
Expert's answer
2022-03-03T17:47:50-0500

y=βˆ’3x+5z,y = -3x + 5z, then the points that are satisfying the equation of the plane:


(x,βˆ’3x+5z,z).(x, -3x + 5z, z).

We need to find two different vectors satisfying above that are not a multiple of each other.


(x,βˆ’3x+5z,z)=x(1,βˆ’3,0)+z(0,5,1).(x, -3x + 5z, z) = x(1, -3, 0) + z(0, 5, 1).

An obvious basis:


{(1,βˆ’3,0),(0,5,1)}.\begin{Bmatrix} (1, -3, 0), (0, 5, 1) \end{Bmatrix}.



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