Recent content by MathNoob22

I can't think of how to prove that any 2x2 matrix left over by omitting one of the columns will be guaranteed to be non-scalar multiples. The matrix I have in mind is: \left( \begin{array}{cc} 3 4 7 \\ 6 8 8 \\ \end{array} \right) \ If I omit column j=3, I'll have a...

Wow, that's actually pretty obvious. If the rows aren't scalar multiples of each other, than the determinant can't possible equal to 0. And if the determinant isn't equal to 0, then the matrix is invertible! One last problem, do we have to prove anything about omitting a column? I thought that...

The ratios should be equal to the constant \beta, but that's assuming that ad-bc=0. If that was the case, then that matrix wouldn't be invertible. Am I misunderstanding something?

I know then that ad-bc\neq0. But I don't know where to go after that. :( I think I have to use the Gram-Schmidt process, but I'm not sure. Help please?

Homework Statement Let A be a 2x3 matrix with real coefficients, and suppose that neither of the two rows of A is a scalar multiple of the other. By quoting an appropriate theorem from linear algebra, show that for some j \in {1,2,3}, the 2x2 matrix obtained by omitting the jth column of A is...

Hello again. Thanks for all the help and advice. This is the new proof I have now. a) Prove that \bar{T} is well defined; that is prove that if v+N(T)=v'+N(T), then T(v)=T(v'). By definition, N(T) is the set of all vectors x in V such that T(x)=0. If v+N(T)=v'+N(T), both cosets have...

Homework Statement Let T: V \rightarrow Z be a linear transformation of a vector space V onto a vector space Z. Define the mapping \bar{T}: V/N(T) \rightarrow Z by \bar{T}(v + N(T)) = T(v) for any coset v+N(T) in V/N(T). a) Prove that \bar{T} is well-defined; that is, prove that if...