Question

2. [1 point] Linear independence: a. Let x1=[1 2 3] , y1=[4 5 6] and z1=[5 7 9]. Are three of them independent? Show which MATLAB command(s) can be used to find out the answer. Also show the results of using the command(s). b. Repeat the process for x2=[1 0 3], y2=[4 5 6] and z2=[5 2 9].

Answer 1

>> %A set of n vectors of length n is linearly independent if the matrix with these vectors as columns has a non-zero determinant >> %matlab command to find determinant of matrix mat is det (mat) >mat-i 4 5:2 5 7:3 6 9 mat- > det (mat) ans 1.3323e-15 >>sthis is 10 to the power of -15, which is o th xl yi and 21 are linearly dependent >>勧 >mat-[1 4 5:0 5 2:3 6 91 mat- > det (mat) ans -18 >> 2 y2 and z2 are linearly independent 兵>>

Command Window >> another method >> %if the row reduced echelon form returns an identity matrix, the vectors are linearly independent >> %matlab command to find row reduced echelon form-rref (mat) >> mat=[1 4 5,2 5 7,3 6 9] mat = 7 >> rref (mat) ans- >> %since it is not identity, these are linearly dependent >> mat=[1 4 5:0 5 2,3 6 9] mat - >> rref (mat) ans - >> %since it is identity, these are linearly independent