Prove that the set of vectors is linearly independent and spans R3.В 3 {(1, 1, 1), (1, 1, 0), (1, 0, 0)}1 11 0 0The matrix0 1 0which shows that the equation c1(1, 1, 1) + c2(1, 1, 0) + c3(1, 0, 0) = (0, 0, 0) has1 1 01 0 0---Select---to0 0 1---Select---. So, the three vectors are linearly independent. Furthermore, the vectors span R3 because the coefficient matrix of the linear system1 1 1C1U11 1 0C2 =U2is ---Select--- v.1 0 0C3U3

the matrix 111110110 reduces to 100010001 which shows that the equation…

***..... Prove that the set of vectors is linearly independent and spans R3. В 3 {(1, 1, 1), (1, 1, 0), (1, 0, 0)} 1 1 1 1 0 0 The matrix 1 1 0 --Select--- v to 0 1 0, which shows that the equation c;(1, 1, 1) + c2(1, 1, 0) + c3(1, 0, 0) = (0, 0, 0) has 10 0 v. So, the three vectors are linearly independent. Furthermore, the vectors span R3 because the coefficient matrix of the linear system 0 0 1 --Select--- 1 1 1 1 1 0 C1 2 = u2 is ---Select--- v . 1 0 0 U3