The equation of the plane is x1 + 3x2 + x3 = 0.murielg said:Homework Statement
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Homework Equations
The Attempt at a Solution
Ok so I know that this plane goes thru the origim
I guess to find the two column vectors that span S, say v1 and v2
That's not possible. You can run a line through any two points on a plane.murielg said:so i need to find two points on that plane that are not in the same line, right?
No, calculate L(v1) and L(v2) to find a basis for L(S). You should already have a basis for S from the work above.murielg said:and then do L(v1) and L(v2) to find the basis for S ?
Finding a basis for the image of a set means finding a set of vectors that span the image of the set. This set of vectors can then be used to represent any vector in the image through linear combinations.
Having a basis for the image of a set allows us to easily represent any vector in the image using a linear combination of the basis vectors. This makes it easier to perform calculations and understand the properties of the set.
To find a basis for the image of a set, we need to first find the image of the set. Then, we can use the image to determine which vectors are linearly independent. These linearly independent vectors form the basis for the image of the set.
Yes, a set can have more than one basis for its image. This is because there can be multiple sets of linearly independent vectors that can span the image of a set.
Finding a basis for the image of a set is related to linear transformations because it allows us to understand the behavior of the set under the transformation. The basis vectors can be thought of as the building blocks for the transformation of the set.