Question

4. Consider the matrix 1 1 0 -1 0 -1 1 3 12 1 1 (a) Use Matlab to determine the reduced row echelon form of A. (b) If v, v2, vs, v4 are the column vectors of the matrix A, use your result from (a) to obtain a basis for the subspace of W-lin[vi, V2, vs, v4. Write the basis in the box below.

please provide the matlab working screenshot

Answer 1

a) Required Matlab code with explanatory comments is given below:

Command Window A= 0 1 0 1 1 2 >> rref (A) ans - 2 x >

b) The fact that the third and fourth columns have no pivot elements, we can say that the column space of matrix A is generated only by the first and second columns

We can also check this by noting that $v_3=-(v_1+v_2),\,v_4=-2v_1-3v_2$

Based on this, we can say that the required basis is:

0112 1 - 01 2