1.II.6B
Let be a real matrix. Define the rank of . Describe the space of solutions of the equation
organizing your discussion with reference to the rank of .
Write down the equation of the tangent plane at on the sphere and the equation of a general line in passing through the origin .
Express the problem of finding points on the intersection of the tangent plane and the line in the form . Find, and give geometrical interpretations of, the solutions.
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