Question

Find the value of x so that that the rank of the matrix
[3х – 8 3
3
3 3x – 8 3 is < 2. Also find the rank
3
3 3x – 8

Answer 1

Answer:

math equation solution

Answer 2

Given:   ∣ 3 x − 8 3 3 3 3 x − 8 3 3 3 3 x − 8 ∣

To find  The value of x and  the rank

Solution: ∣ 3 x − 8 3 3 3 3 x − 8 3 3 3 3 x − 8 ∣  

|3x−83333x−83333x−8| = 0

Let Δ =  ∣  ∣ 3 x − 8 3 3 3 3 x − 8 3 3 3 3 x − 8 ∣  ∣ |3x−83333x−83333x−8|

We need to find the roots of Δ = 0.  

.  Applying C1→ C1 + C2, we get Expanding the determinant along C1, we have Δ = (3x – 2)(1)[(3x – 11)(3x – 11) – (0)(0)]

⇒ Δ = (3x – 2)(3x – 11)(3x – 11)

∴ Δ = (3x – 2)(3x – 11)2   The given equation is Δ = 0.

⇒ (3x – 2)(3x – 11)2 = 0   Case – I :  3x – 2 = 0  

⇒ 3x = 2 ∴ x =  2 3 23    Case – II : (3x – 11)2 = 0  ⇒ 3x – 11 = 0

⇒ 3x = 11  

∴ x =  11/ 3

Thus,  2/ 3  and  11 /3 are the roots of the given determinant equation.