linear eqs and geometry

solution possibilities for two lines in R²

one solution at an intersection point, no solutions for parallel lines, infinitely many solutions for overlapping solutions

system of eq in three variables means

planes ; one solution at a point, no solutions when they’re parallel stacked, infinitely many when they combine at a line

a linear eq in variables a1x1 + a2x2 +…+anxn = b represent a _

hyperplane, an (n-1)-dimensional object in space Rⁿ

linear system characteristics

coefficients can be zero, aij called coefficients, bi called constants