This is Differential equation Math Please write the all step

This is Differential equation Math. Please write the all steps ( Please typing only ) don\'t don\'t on paper

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Solution

Given vectors can be written in matrix form as

[ 3 6 10
1 2 3
3 0 9]
Deteminent of above= 3(18-20)+9(6-6)
=3*-2=-6
Which is not zero hence rank is 3
It contains 3 variables
Hence it is linearly independent.