1.4.30 Matrix Transformations

Condition: let \ (a_ {1}, a_ {2}, \ ldots a_ {n+1}- \) size matrices \ (n \ times n \). To prove that there are \ (n+1 \) numbers \ (x_ {1}, x_ {2}, \ ldots, x_ {n+1} \), not equal to zero at the same time, such that the matrix \ (x_} a_ {1}+\ cdots+x_} a_ {n+1} \) Refined.