3 S 0 02 Rx d 5 is S in 1 You must support your answer C1 C ER a 12 points Find a 3 x 4 reduced echelon matrix R and a vector d

Question

3 S 0 02 Rx d 5 is S in 1 You must support your answer C1 C ER a 12 points Find a 3 x 4 reduced echelon matrix R and a vector d E R such that the solution set of the linear system 1 b 5 points Suppose that the augmented matrix R d of the linear system Rx d that you determined in part a in reduced echelon form is obtained from the augmented matrix A b of another linear system Ax b by first subtracting 3 times the first row from the second row then subtracting 5 times the second row from the third row Find the 3 x 4 matrix A and the vector b E R Show the details of your work c 8 points Now consider any linear system Cx f for some 4 x 4 matrix C and vector fER whose solution set is S in 1 Is the set consisting of columns of C linearly independent Why or why not

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