About this video
This short hint video finds the determinant of the 2x2 matrix [[5, 3], [-1, 4]]. It multiplies the main diagonal (5 x 4 = 20) and subtracts the product of the other diagonal (3 x -1 = -3), giving 20 - (-3) = 23.
You'll be able to
- find the determinant of a 2x2 matrix as ad - bc.
- handle negative entries correctly when subtracting the second diagonal product.
Key words
- determinant
- A single number calculated from a square matrix; for [[a, b], [c, d]] it is ad - bc.
- diagonal
- A line of entries in a matrix running from one corner to the opposite corner.
Transcript
As a hint, I'll take the determinant of a very similar two by two matrix. So we wanna figure out the determinant of this matrix and we can denote it by the determinant of the 2x2 matrix five, three,negative one and four and the definition of determinant of the 2x2 matrix like this, as we can first take this diagonal, five times four so write it down, just going to be equal to 5 * 4 minus of product of that diagonal ...so what is this give us? So, five times four is twenty and then three times negative one will be negative three this is negative three...
but making negative the negative three will make the positive three so the determinant of this matrix is twenty three.
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