Q. 475.0( 1 Vote )

# Show that where a,b,c are in A.P.

Let Recall that the value of a determinant remains same if we apply the operation Ri Ri + kRj or Ci Ci + kCj.

Applying R1 R1 + R3, we get  Given that a, b and c are in an A.P. Using the definition of an arithmetic progression, we have

b – a = c – b

b + b = c + a

2b = c + a

a + c = 2b

By substituting this in the above equation to find Δ, we get  Taking 2 common from R1, we get Applying R1 R1 – R2, we get  Δ = 0

Thus, when a, b and c are in A.P.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Determinants of Matrices of different order59 mins  Determining a determinant63 mins  Types of Matrices & Properties51 mins  Triangular Matrices & operations on matrices58 mins  Know About finding the Adjoint & Inverse Of Matrix46 mins  Interactive Quiz on Properties of Determinants43 mins  Lecture on Product of Determinants58 mins  Test Yourself, Properties of Determinants30 mins  Interactive Quiz on Matrices & Determinants48 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 