Machine Learning Foundations

Week 3: Open Session

  1. \(x=(1, 2, 3)\)
  2. \(y=(1,-1,1)\)

The linear combinations of \(v = (1, 1, 0)\) and \(w = (0, 1, 1)\) fill a plane in \(\mathbb R^3\).

  1. Find a vector that is not a combination of \(v\) and \(w\) (i.e. not on the plane).
  2. Find a vector perpendicular to that plane

For the vectors \(v = ( 3, 4)\) and \(w = ( 4, 3)\) test the Cauchy-Schwarz inequality and find whether they satisfy or not.

True or false.

  1. The vectors \(b\) that are not in the column space \(C(A)\) form a subspace.
  2. If \(C(A)\) contains only the zero vector, then \(A\) is the zero matrix.
  3. The column space of \(2A\) equals the column space of \(A\).
  4. The column space of \(A - I\) equals the column space of \(A\).

False

False

True

True

Do you know him?

Alan Mathison Turing

Turing test, an attempt to define a standard for a machine to be called "intelligent".

John McCarthy

The term artificial intelligence was first coined in 1956 at the Dartmouth conference organized by him.

Week 3: Open Session

By Amrutha

Week 3: Open Session

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