Question

Use Cramer’s rule to solve for x: x + 4y − z = −14 5x + 6y + 3z = 4 −2x + 7y + 2z = −17

Answer 1

Answer:

Solve using determinants:

x + 4y − z = −14  

5x + 6y + 3z = 4  

−2x + 7y + 2z = −17  

|A| =  -120  

|Ax| =  -240

|Ay| = 360  

|Az| = -480  

x =  2

y = -3    

z =  4

Step-by-step explanation:

Solving a 3 x 3 Linear System Using Cramer's Rule

Answer 2

Answer:

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