4 5 3] B= [ -3 1 -4 2] C= [3 3 3 3] and D= [ 0 -2 2 -3] Determine if the vectors

Question

                4

                5

                3]

B= [ -3

        1

        -4

        2]

C= [3

       3

       3

       3]

and D= [  0

                -2

                2

               -3]

Determine if the vectors are linearly independent or linearly dependent. If they are linearly dependent, determine a non-trivial linear relation -(a non-trivial relation is three numbers which are not all three zeros) Otherwise, if the vectors are linearly independent, enter 0's for the coefficients, since the relationship always holds.

Write in this form: _____A + _____B+ _____C+ ______D =0

Explain briefly why?

Explanation / Answer

they are linearly independent .

let x1,x2,x3,x4 be such that x1A+x2B+x3C+x4D = 0,

solving for equations gives (0,0,0,0) as the only solution, hence they are linearly independent

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