Question

please help on answering ANS1=

Start Typing in MATLAB 1 2 3 Example 1: Let B = | 40 il Type : B = 1 2 3:4 01. Before continuing using MATLAB consider the set of all linear combinations of the row vectors of B. This is a subspace of Rspanned by the vectors rı = [1 2 3] and r2 = ( 4 0 1]. First note that the two vectors r i and r2 are linearly independent (Why?). Enter your answer as: % ANS1= type your answer So these two vectors rı and r2 form a basis for the row space of B. Since B is a simple matrix of small size, you should also be able to justify that the row space of B is a subspace of R3 but it is not RS, which means that row vectors of B do not span R. In other words there are vectors in R which are not in the row space of B. For large matrices finding out this information is not that simple. You could get some information about the dimension of the row space or column space using the size of the matrix. Another useful MATLAB command is rref(B).

Answer 1

ANS1. The vectors r1 and r2 are linearly independent because there is no linear combination of either r1 or r2 that converts r1 into r2 and vice versa. Hence the two vectors r1 and r2 are linearly independent.