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3. Consider the following system of linear equations: 2x + 2y + 2kz = 2 kx + ky+z=1 2x + 3y + 7z = 4 (i) Turn the system into row echelon form. (ii) Determine which values of k give (i) a unique solution (ii) infinitely many solutions and (iii) no solutions. Show your working.
2. Let v= [6, 1, 2], w = [5,0, 3), and P= (9, -7,31). (i) Find a vector u orthogonal to both v and w. (ii) Let L be the line in R3 that passes through the point P and is perpendicular to both of the vectors v and w. Find an equation for the line L in vector form. (iii) Find parametric equations for the line L.
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