System x1 + 3x2 = k and 4x1 + hx2 = 8 has unique solution if h = 12. Vectors containing zero vector are linearly dependent. Matrix A does not span R4
Echelon form requires nonzero rows above zero rows. Each leading entry of a row is in a column to the right. All entries below a leading entry are zero. Reduced echelon form adds leading 1s to nonzero rows
Gaussian elimination solves systems of linear equations using row-wise operations. Algorithm transforms matrix into row echelon form by filling lower left corner with zeros. Three types of elementary row operations: swapping, multiplying, adding. Matrix is in reduced row echelon form when all leading coefficients are 1
A linear system consists of two or more equations involving the same variables. A solution is an assignment of values that satisfies all equations simultaneously. Linear systems are fundamental in modern mathematics and engineering
Kernel is the part of domain mapped to zero vector of co-domain. Kernel is always a linear subspace of domain. Two elements have same image if their difference lies in kernel. Kernel is orthogonal complement to row space of matrix
Intersection is the set containing all elements present in two or more objects. In set theory, intersection means overlapping area of objects. In geometry, intersection can be point, line, or curve