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Homework Statement
Determine whether the set is a basis for R3.
[3, -8, 1] , [6, 2, -5]
The Attempt at a Solution
I know it does not span R3, but the book says it is a basis for a plane in R3. How is it a plane?
A basis for R3 is a set of three vectors that are linearly independent and span the three-dimensional space. This means that any vector in R3 can be written as a linear combination of these three vectors.
To determine if a set of vectors is a basis for R3, you can use the following criteria:
The numbers in the vectors represent the coordinates of each vector in a three-dimensional space. The first number represents the x-coordinate, the second represents the y-coordinate, and the third represents the z-coordinate.
No, a set of two vectors cannot be a basis for R3. This is because a basis for R3 must contain three linearly independent vectors in order to span the three-dimensional space.
Having a basis for R3 allows us to represent any vector in three-dimensional space as a linear combination of the basis vectors. This is useful in many areas of mathematics and science, such as in solving systems of linear equations and in studying three-dimensional objects and phenomena.