Question

(b)
Solve by Cramer's rule :
x+y+z=6
2x+ 5y + 5z = 27
2x + 5y +11z=45

​

Answer 1

Explanation:

x+y+z=6,2x+5y+5z=27,2x+5y+11z=45

Answer 2

Given,

x+ y+ z = 6

2x+ 5y+ 5z = 27

2x+ 5y + 11z = 45

To find,

The value of x, y, and z by using Cramer's Rule.

Solution,

The value of x,y, and z are 1,2, and 3 respectively.

We can simply solve the mathematical problem by the following procedure.

We know by Cramer's Rule that,

x = Δ₁/Δ

y = Δ₂/Δ

z = Δ₃/Δ

only when Δ is not equal to zero.

Thus,

Δ = $\left[\begin{array}{ccc}1&1&1\\2&5&5\\2&5&11\end{array}\right]$

   = 1 (55 - 25) -1 ( 22 - 10) + 1(10-10)

   = 30 - 12

   = 18

Δ₁ = $\left[\begin{array}{ccc}6&1&1\\27&5&5\\45&5&11\end{array}\right]$

    = 6(55-25) - 1(297 - 225) +1(135 - 225)

    = 180 - 72 - 90

    = 18

Δ₂ = $\left[\begin{array}{ccc}1&6&1\\2&27&5\\2&45&11\end{array}\right]$

    = 1(297 - 225) - 6(22 - 10) + 1(90 - 54)

    = 72 - 72 + 36

    = 36

Δ₃ = $\left[\begin{array}{ccc}1&1&6\\2&5&27\\2&5&45\end{array}\right]$

    = 1(225 - 135) - 1(90-54) + 6(10-10)

    = 90 - 90 + 54

    = 54

Now,

x = Δ₁/Δ

  = 1

y = Δ₂/Δ

  = 2

z = Δ₃/Δ

  = 3

Thus,

The value of x,y, and z are 1,2, and 3 respectively.