Write the next five numbers in each sequence,a 1000, 3 000, 5 000,b 12 000, 13 000, 14 000,c 24 000, 23 000, 22 000,d 32 000, 42 000, 52 000,e 23 500 ,23 000, 22 500,​

Answer:SOLUTION First, we write the augmented matrix. ⎡ ⎢ ⎣ 1 − 1 1 2 3 − 1 3 − 2 − 9  |  8 − 2 9 ⎤ ⎥ ⎦ Next, we perform row operations to obtain row-echelon form. − 2 R 1 + R 2 = R 2 → ⎡ ⎢ ⎣ 1 − 1 1 0 5 − 3 3 − 2 − 9 | 8 − 18 9 ⎤ ⎥ ⎦ − 3 R 1 + R 3 = R 3 → ⎡ ⎢ ⎣ 1 − 1 1 0 5 − 3 0 1 − 12 | 8 − 18 − 15 ⎤ ⎥ ⎦ The easiest way to obtain a 1 in row 2 of column 1 is to interchange \displaystyle {R}_{2}R ​2 ​​  and \displaystyle {R}_{3}R ​3 ​​ . Interchange R 2 and R 3 → ⎡ ⎢ ⎣ 1 − 1 1 8 0 1 − 12 − 15 0 5 − 3 − 18 ⎤ ⎥ ⎦ Then − 5 R 2 + R 3 = R 3 → ⎡ ⎢ ⎣ 1 − 1 1 0 1 − 12 0 0 57 | 8 − 15 57 ⎤ ⎥ ⎦ − 1 57 R 3 = R 3 → ⎡ ⎢ ⎣ 1 − 1 1 0 1 − 12 0 0 1 | 8 − 15 1 ⎤ ⎥ ⎦ The last matrix represents the equivalent system.  x − y + z = 8  y − 12 z = − 15  z = 1 Using back-substitution, we obtain the solution as \displaystyle \left(4,-3,1\right)(4,−3,1).Step-by-step explanation: