Find an equation of the plane that equals span are given an explicit description

Question

Find an equation of the plane that equals span are given an explicit description of a suhspace and are as description of the same suhspace.. In this problem you ced to find an implicit 2. The plane through the origin that satisfies the equation 3i + 2t/-z = 0isa subspace of R3. Describe this subspace explicitly as the span of a two-vector set. In this problem you are given an implicit description of a subspace and asked for an explicit description of the same subspace. 3. Find symmetric equations for the line that equals span In this problem

Explanation / Answer

1) Since it is vector space plane passes through origin

let ax + by +cz = 0 be the equation.

a+3b + c = 0

2a + b + c = 0

a = 2b

c = -5b

eq is :

2x +y -5z =0

2) take x=y=1

z = 5

plane passes through [1,1,5]

take x = 0, y= 1

z = 2

plane passes through [0,1,2]

c) [x,y,z] =lambda [4,3,2]

x = 4 lambda

y= 3lambda

z = 2 lambda

x/4 = y/3 =z/2 = lambda

4) x+3y+z = 0

x + 4y +3z = 0

y = -2z

x = -z

[1,2,-1] is the subspace of line

5) 3x+2y=0

x=-2/3y

[2,-3]

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