Linear Dependence

p {margin: 0; padding: 0;} No. Date Linear dependence 1) A set of vectors is linearly dependent if any one of them can be expressed as a linear combination of the remaining vectors otherwise it is linearly independent 2) Formal definition : Linear independence (LI) The set {u. unis is called a linearly independent cas of vechos TE c, a + + c. n. = o c, C2 C. = 0 Notes: - Dependence prevents solving a system of equations More unkwon than independent equations - The number of linearly independent rowrs or columns in a. matrix is the rank of a matrix (rank (A)) Examples: vi 5 12] V', : 10 24 5 10 v'l = 12 24 v'2 2v' - V'2 , o' V, = 2 i V2 = / ; V3 4 7 8 5 3v,-2v 2 = [6 21] - [2 16] [a s] = V3 3v1 - 2V2 - V3 =0