I have the following problem: 1) (1,1,2) is a basis for the row space. 2) (1,2) is a basis for the columns space.
I tried to find orthogonal vectors to the given basis, but the solution manual says that they are orthogonal because the space is only consisting of only one vector.
Can someone explain me how this works? I feel more confused after this problem..
Thanks!
An orthonormal basis is - by definition - a basis, in which all the basis vectors are parwise orthogonal, with the length 1.
Since there is only one basis vector, it's obviously also "orthogonal with the other basis vectors" - since there is not any. This means by definition, that it is an orthonormal basis IF you just normalise it by dividing it by it's length. Hope this helps :-)