1.ya.21 Linear spaces
condition: For a given matrix, find the basis and dimension of the row space, column space and kernel. a) \( \left(\begin{array}{cccc}1 & 4 & -4 & 2 \\ 3 & 12 & -12 & 6 \\ 1 & 4 & -4 & 2\end{array}\right) \) b) \( \left(\begin{array}{ccccc}-2 & -2 & -13 & 1 & 7 \\ -4 & 16 & 4 & -18 & 14 \\ -2 & 4 & 14 & -11 & -5 \\ -8 & 8 & 5 & -23 & 6\end{array}\right) \)
Linear spaces, subspaces. Investigation of given sets with operations defined on them to compose a linear space. Axioms of linear spaces. Linear spaces of polynomials, matrices, vectors, functions and numbers.