Are the vectors - -3 0 3 -2 5 -4 4 1 3 5 2 and 2 1 4 linearly independent?

isto 5 4 3 2 - 4c = < 1 5 -4 -3 -2 -1 -1 -2 wŃ -3 -4 1 2 3 4 Find the components of the vector -4c based on the vector shown.

why is it not all 4 vectors span W?

Show that the column vectors (1,1,2,4), (2,-1,-5,2). (1,-1,-4,0and (2,1,1,6) vectors in R are linearly dependent.

Orthonormalize the following set of three vectors: {(1, -1, 2), (1, 3, 1), (1, 0, 2)}. Please use legible handwriting and also please explain each step clearly. Thank you!

The zero vector 0 = (0, 0, 0) can be written a linear combination of the vectors v., v,, and v- because 0 = Ov, + 0v, + 0v3. This is called the trivia! solution. Can you find a nontrivial way of writing 0 as a linear combination of the three vectors? (Enter your answer in terms of v., v,, and v- If not possible, enter IMPOSSIBLE.) V1 = (1, 0, 1), V2 = (-1, 1, 2), V3 = (0, 1, 6)

Solve the system below. Parameterize the solution set. – 2x + Зу + 3y 7z 4х + 7y + 19z 11 - 6x 6y 6z - 12 - +

Let be the vector with initial point (4, 7) and terminal point (8,4). Express as a linear combination of the standard unit vectors. Ov=-3i+47 Ov=-4i +37 Ov=41-37 Ov=4i +3j Ov=-41-3j O None of the above.

Express the vector b = a₁ + a1 a₂ + a2 2 = -4 as a linear combination of the vectors a₁ 5 a3 = b -2 3 7 " a2 = Гот 1 0 > a3 = 3

Show that the column vectors (1,1,2,4), (2,-1,-5.2), (1.-1,-4,0) and (2,1.1,6) vectors in R are linearly dependent.