Determine if the vectors v1 = (2, −1, 0, 3), v2 = (1, 2, 5, −1), v3 = (7, −1, 5, 8) are linearly independent vectors in r4 .

if the vectors in problem above are linearly dependent, write v1 as linear combination of two other vectors.

Answer with Step-by-step explanation:

We are given that three vectors

We have to determine the given vectors are linearly independent in and write as linear combination of other two vectors if the vectors are dependent.

To find the linearly dependent we will use matrix.

If m=Number of rows, n=Number of columns then,

Rank of matrix=min(m,n)

Rank of matrix=min(3,4)

Rank of matrix=3

Dimension of

Rank

Therefore, it is linearly  dependent .

so the possibilities of the measurement of the side of the triangle are either it is longest side or not the longest side

when it is the longest side

s < 25 + 35s < 60

if it is not the longest side

35 < 25 + s10 < sso 10 < s < 60so the perimeter70 < p < 130