Question

⎧⎣⎡p−5q3p+4r−5q+9r−3p+6r⎦⎤ ;p,q,r in R ⎭⎬⎫ Find a basis for the subspace. A basis for the subspace is (Use a comma to separate answers as needed.)

Answer 1

To find a basis for the given subspace, we need to determine a set of vectors that span the subspace and are linearly independent. The possible basis for the subspace is (-2, 0) and (0, 7).

Step-by-step explanation:

The question is asking for a basis for the subspace represented by the expression p-5q/(3p+4r)-5q+9r-(3p+6r). To find a basis, we need to determine a set of vectors that span the subspace and are linearly independent.

First, let's simplify the expression:

p-5q/(3p+4r)-5q+9r-(3p+6r) = p-5q/3p+4r-5q+9r-3p-6r = -2q+7r

Now, we can choose two independent vectors that span the subspace. A possible basis is (-2, 0) and (0, 7).