x + 4y − z = −14 5x + 6y + 3z = 4 −2x + 7y + 2z = −17

A = -120 AX = -240 X = 2 Step-by-step explanation: ∵ x + 4y - z = -14 ∵ 5x + 6y + 3z = 4 ∵ -2x + 7y + 2z = -17 \left[\begin{array}{ccc}1&4&-1\\5&6&3\\-2&7&2\end{array}\right]=\left[\begin{array}{ccc}-14\\4\\-17\end{array}\right] ∴ A = 1(6×2 - 3×7) + (-4)(2×5 - 3×-2) + (-1)(5×7 - 6×-2) ∴ A = 1(12 - 21) + (-4)(10 - -6) + (-1)(35 - -12) ∴ A = -9 + (-4)(16) + (-1)(47) = -9 - 64 - 47 = -120 To find X replace the column of X by the column of the answer \left[\begin{array}{ccc}-14&4&-1\\4&6&3\\-17&7&2\end{array}\right] ∴ AX = -14(6×2 - 3×7) + (-4)(4×2 - 3×-17) + (-1)(4×7 - 6×-17) ∴ AX = -14(12 - 21) + (-4)(8 - -51) + (-1)(28 - -102) ∴ AX = 126 + (-4)(59) + (-1)(130) = 126 - 236 - 130 = -240 ∴ X = AX/A = -240/-120 = 2