Your dose of math nonsense of the day.

• A system of linear equations has either one, infinitely many or no solution(s).

• The link between rank and linear independence is one of the most amazing aspects of linear algebra. The rank shows how many linearly independent column/row vectors a matrix has.

• Two vectors are linearly independent iff they do not lie on the same line.

• All real numbers are linearly dependent – they can be expressed as linear combination of each other; scalar multiples of each other and/or multiples of one (the latter being the case of primes).

• Imaginary numbers are of general form α + βi where i is the square root of negative one. Imaginary numbers come in conjugate pairs.