Exercises 51 through 60 are concerned with conics. A conic is a curve in M2 that can be described by an equation of the form fix, y) = cj + c2x + c3y + c4x2 + csxy + C6y2 = o, where at least one of the coefficients c, is nonzero. Examples are circles, ellipses, hyperbolas, and parabolas. If k is any nonzero constant, then the equations f(x, y) = 0 and kf(x, y) = 0 describe the same conic. For example, the equation -4 + x2 + y2 = 0 and 12 + 3x2 + 3y2 = 0 both describe the circle of radius 2 centered at the origin. In Exercises 51 through 60, find all the conics through the given points, and draw a rough sketch of your solution curve(s). (0,0), (1,0), (0,1), and (1,1).

1.7 Linear Independence n - An indexed set of vectors {v ,…,1 } ip R is said to be linearly independent if the vector equation + + ⋯+ = 0 has only the trivial solution. ▯ ▯ ▯ ▯ ▯ ▯ The set {v 1…,v p is said be linearly dependent if their exist weights c 1…,c p not all zero, such that ▯ ▯+ ▯ ▯ ⋯+ =▯ ▯ - + + ⋯+ = 0 à linear dependence relation amount v ,…,v , when ▯ ▯ ▯ ▯ ▯ ▯ 1 p the weights are not all zero Linear Independence of Matrix Columns - The columns of a matrix A are linearly independent if and only