Question

Find the inverse

Please help me solve this problem step-by-step. I am brand new to this material and confused. The first set of items is an example, the bottom matrix is the one I'm confused on how to solve. Any help would be much appreciated!

[1 0 -2] Ex. Find the inverse of the following matrix -3 1 4 using elementary row operations. | 2 - 34 | Shown below are elementary row matrices that when multiplied transform A into the identity matrix. If one uses the method of finding the inverse of A by reducing A to I via elementary row operations and tracks these operations: The first operation would have been to replace R2 with 3R1 + R2. The second operation would have been to replace R3 with -2R1 + R3. The third operation would have been to replace R3 with 3R2 + R3. The fourth operation would have been to multiply R3 by %. The fifth operation would have been to replace R1 with 2R3 + R1. The sixth operation would have been to replace R2 with 2R3 + R2. 1 0 0 1 0 21 1 0 0 1 0 0 0 0 1 0 0 1 8 3 11 0 1 2 0 1 0 0 1 0 0 1 0 1 0 1 0 3 1 0 = 10 4 1 LO O O O 1 0 0 0 3 1] |-2 0 1 0 0 1] 3.5 1.5 0.5 And, 18 3 11i 0 -2] [1 0 01 10 4 1 -3 1 4 - 0 1 0 (3.5 1.5 0.5] | 2 -3 4 0 0 1 You try: Find the inverse of 13 -4 11 2 -1 1 4 -7 -3

Answer 1

Given ment with a 2x 3 mahin To 2 -1 1 1 0 1 0 A Reduce matic to row echelon form ! e 14-7 -3 10 oil ! L3 -4 11 100 1 R2 + Rz-IR R₂ < Rp - 14 -7 -3 o sla slo 0 0 1 OL- Ryt Rs -1 14 -7 -3 rooi

Now Conver Reduced manu to reduced low echelon Form R3 < 1 R3 i 4 -7 o 1/2 -3/4 '' ] -5/ 01- 1512 You Too !! Va V - Vy R, TR, +3R3 Rex R2 - SR - P22 Z Rz t rio o il 1%0% ] Q,+ 7Rzelo o Va 13.92 You ŹR, O 01Ya -Yu Y Ars Inverse - (- ve 19% 9%] 1/20 20 c