Solve linear system?

Question

Sovle with matrices.
SHOW ALL WORK.

10x+6y-4z=454
43x+-24y+30z=1625
17x+144y+145z=42050


Have fun!

Answer 1

10 6 -4 | 454
43 -24 30 | 1625
17 144 145 | 42050

Step 1: Multiply line 1 by -4.3, and add to line 2.
43 -24 30 | 1625 (2)
-43 -25.8 17.2 | -1952.2 (-4.3 * 1)
0 -49.8 47.2 | -327.2 (4)

Step 2: Multiply line 1 by -1.7, and add to line 3.
17 144 145 | 42050 (3)
-17 -10.2 6.8 | -771.8 (-1.7 * 1)
0 133.8 151.8 | 41278.2 (5)

Step 3: Multiply line 4 (from step 1) by 133.8/49.8 and add to line 5 (from step 2)
0 -133.8 6315.36/49.8 | -43779.36/49.8 (133.8/49.8 * 4)
0 133.8 151.8 | 41278.2 (5)
0 0 13875/49.8 | 2011875/49.8 (6)

Step 4: Solve line 6 for y:
0 0 13875/49.8 | 2011875/49.8 (6)
0 0 13875 | 2011875
0 0 1 | 145 (7)

Step 5: Multiply line 7 (from step 4) by -12.8 and add to line 4.
0 -49.8 47.2 | -327.2 (4)
0 0 -47.2 | -6844 (-47.2 * 7)
0 -49.8 0 | -7171.2 (8)

Solve line 8:
0 -49.8 0 | -7171.2 (8)
0 1 0 | 144 (9)

Step 6: Add -6 * line 9 and -4 * line 7 to line 1.
0 -6 0 | -864 (-6 * 9)
0 0 4 | 580 (-4 * 7)
10 6 -4 | 454 (1)
10 0 0 | 170 (10)

Solve line 10:
10 0 0 | 170 (10)
1 0 0 | 17 (11)

Step 7: Take line 7, 9, and 11 to create an identity matrix:
1 0 0 | 17 (11)
0 1 0 | 144 (9)
0 0 1 | 145 (7)

Check:
10x+6y-4z=454
10 * 17 + 6 * 144 - 4 * 145 = 454 (check!)

Answer 2

I thin you spelled mattress wrong.8-D