wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Let α,β and γ be real numbers such that the system of linear equations
x+2y+3z=α
4x+5y+6z=β
7x+8y+9z=γ1
is consistent.
Let |M| represent the determinant of the matrix M=α2γβ10101.
Then the value of |M| is

Open in App
Solution

Δ=∣ ∣123456789∣ ∣
R3R3R1, R2R2R1
Δ=∣ ∣123333666∣ ∣
Δ=0
Given system of equation will be consistent even if α=β=γ1=0,
i.e., equations will form homogeneous
system.
So, α=0,β=0,γ=1
|M|=∣ ∣021010101∣ ∣
|M|=1

flag
Suggest Corrections
thumbs-up
11
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon