Question

Determine whether the members of the given set of vectors are linearly independent. If they are linearly dependent, find a linear relation among them of the form c1x(1) + c2x(2) + c3x(3) = 0. (Give c1, c2, and c3 as real numbers. If the vectors are linearly independent, enter INDEPENDENT.) x(1) = 9 1 0 , x(2) = 0 1 0 , x(3) = −1 9 0

Answer 1

Step 1:

The given vectors are:

Step 2: Set up a homogeneous system of equations, we get:

Step 3:

Thus, we get the homogeneous system of equations:

Step 4:

The Matrix of Coefficients is given by:

Step 5:

Reduced Row Echelon Form is given by:

Step 6:

Thus, we get the system of equations:

               (1)

            (2)

Step 7:

Since the3nd equation is 0 = 0:

the vectors:x₁, x₂ and x₃ are linearly dependent.

So,

Choose:

From (1):

From (2):

Thus,the answer is:

(i)

the vectors:x₁, x₂ and x₃ are linearly dependent.

(ii)