Question

prove that the function 1,x,x² are lineary independent hence from the differential equation whose roots are 1,x,x²​

Answer 1

Answer with Step-by-step explanation:

We are given that function $1,x,x^2$ are the roots of differential equation

We have to show that $1,x,x^2$  are linearly independent.

Linearly independent function: Those functions  in which any function is not a linear combination of other functions in given set of functions.

We are forming a matrix from the coefficient of given set of functions

A=$\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]$

Any row or column is not a linear combination of other two rows or columns.

Therefore, rank of given matrix=3

Hence, $1,x,x^2$ are linearly independent .

Answer 2

Answer:

Step-by-step explanation: