MATH125 Lecture Notes - Lecture 18: Linear Independence, Distributive Property, Transpose

• School: University of Alberta
• Department: Mathematics
• Course: MATH125
• Professor: Nikita

Document Summary

, ak be matrices of the same size. We de ne their span as the set of all linear combinations of the matrices. , ak of the same size are linearly independent if the system c1a1 + c2a2 + . + ckak = 0 has a unique solution c1 = . If this system has more than one solution we say that the matrices are linearly dependent. Check if the matrices a, b, c from the above example are linearly independent. The system c1a + c2b + c3c = 0 is of the form c1[ Thus the only solution is c1 = c2 = c3 = 0, hence the matrices are linearly independent. Whenever we meet matrix multiplication we must be careful. 1 2 ] , b = [ 1 0. Thus we see that in general (in contrast to addition) one has ab = ba. Also one can easily check that a2 = 0.