MathProblemsBank

1.Ya.21 Linear Spaces

Condition: For this matrix, find the basis and dimension of the space of the lines, the space of columns and nuclei. a) \ (\ legin {Array} {cccc} 1 & 4 &4 &4 & 2 & 2 & 12 & -12 & 6 & & 4 & 4 &4 & 2 \ End {Array} \ Right) \) \ ( \ Left (\ Begin {Array} {CCCC} -2 &2 & -2 &13 & 1 & 7 &4 &4 & 4 & -18 &18 & 14 & 2 & 2 & -14 & -11 & -5 \\ -8 & 5 & -23 &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.