Question

2x-y+3z=5
4x + 2y - z=2
-x+3y + z = 5 using cramers rule​

Answer 1

Step-by-step explanation:

Given as 6x + y – 3z = 5 x + 3y – 2z = 5 2x + y + 4z = 8 Suppose there be a system of n simultaneous linear equations with n unknown given by Suppose Dj be determinant observe from D after replacing the jth column So, Provide that D ≠ 0 Here 6x + y – 3z = 5 x + 3y – 2z = 5 2x + y + 4z = 8 On comparing with theorem, let's find D,D1,D2 and D3 On solving determinant, expanding along 1st row ⇒ D = 6[(4) (3) – (1) (– 2)] – 1[(4) (1) + 4] – 3[1 – 3(2)] ⇒ D = 6[12 + 2] – [8] – 3[– 5] ⇒ D = 84 – 8 + 15 ⇒ D = 91 On solving D1 formed by replacing 1st column by B matrices Here On solving determinant, expanding along 1st row ⇒ D1 = 5[(4) (3) – (– 2) (1)] – 1[(5) (4) – (– 2) (8)] – 3[(5) – (3) (8)] ⇒ D1 = 5[12 + 2] – 1[20 + 16] – 3[5 – 24] ⇒ D1 = 5[14] – 36 – 3(– 19) ⇒ D1 = 70 – 36 + 57 ⇒ D1 = 91 On solving D2 formed by replacing 1st column by B matrices Here On solving determinant ⇒ D2 = 6[20 + 16] – 5[4 – 2(– 2)] + (– 3)[8 – 10] ⇒ D2 = 6[36] – 5(8) + (– 3) (– 2) ⇒ D2 = 182 On solving D3 formed by replacing 1st column by B matrices Here Solving determinant, expanding along 1st Row ⇒ D3 = 6[24 – 5] – 1[8 – 10] + 5[1 – 6] ⇒ D3 = 6[19] – 1(– 2) + 5(– 5) ⇒ D3 = 114 + 2 – 25 ⇒ D3 = 91

so by carame's rule