Homework SourseDetermine whether the rows of A form a linearly dependent se
Determine whether the rows of A form a linearly dependent set. If so, find the nonzero coefficients c1, c2, c3, and c4 involved in a linear combination of rows r1, r2, r3, and r4, respectively, that is zero. Use the techniques in Section 1.3. (If an answer does not exist, enter DNE.)
Solution
The rows will be linearly independent if the given function goes to zero only when all the constant are zero i.e. c1,c2,c3 and c4
c1*r1 + c2*r2 + c3*r3 + c4*r4 = 0
on substituting the rows we get the four equation as below
c1*(3,2,-1,-1) + c2*(2,1,1,2) + c3*(-1,3,2,-9) + c4*(2,-10,-4,30) = (0,0,0,0)
Rearranging the left hand side yields
Hence the vectors doesn\'t lead to identity matrix on row echleon decomposition henece the vectors are linearly dependent
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