How to Tell if Vector Spans R3
You need three vectors to span R3 you have two so the answer is no. A set of vectors from R³ will span R³ if it is a basis set that is to say that it should be a linearly independent set such that each every element x R³ can be written as a linear combination of the elements from this set. Determine If The Unit Sphere Is A Subspace Of The Vector Space R 3 Maths Exam Math Videos Algebra If v xyz reduce the augmented matrix to 2 4 1 2 4 x 0 1 1 x y 0 0 0 7x11y z 3 5. . Put the three vectors into columns of a 3x3 matrix then reduce. Recall that any three linearly independent vectors form a basis of R3. Its a years since I took Linear Algebra so I give no guaranties. If r3 and the vectors are in R3 then this must be the whole space. Support Author Jonathan David. I could have c1 times the first vector 1 minus 1 2 plus some other arbitrary constant c2 some scalar times the second vector 2 1 2 plus some third scaling vector time...