Suppose the row echelon form of a system of equations is x−2y−9z == −10 y+2z == −1 Enter the components of x,y,z using t for the free variable z - ?,?,? (Enter the components of the vector ⟨x,y,z⟩⟨x,y,z⟩, using tt for the free variable)

Write a vector equation 81-8181-81 y+ that is equivalent to the system of equations: -2x + 6y + 7z 2x +9y + 7% + Y x 4 = -9 6% = -6 = =

Consider the following vectors: u = (1, −2, −1), v = (-2, 1, 8) Without using the cross product, find a vector n which is orthogonal to both u and U. You need to use a notion from chapter 5 to set up a system of linear equations, then use RREF to solve the system. Explain why this method works.

The vectors -3 -3 -9 w 3= 12 20 + k 15 are linearly independent if and only if k +