Question

Bonus Question for undergraduates (20 points). Mandatory for grad- uate students what is the determinant of the following matrices. Construct any example and find its determinant if it exists. (a) 2 x 3 matrix (b) Upper triangular matrix (c) 2 x 2 matrix

Answer 1

2x3 matrix d e f we com not find its determinant bez determinat is only defined for square madrices, Determinant mean to repersent size of the - dimensional hyperspace occupied by the redim bectangular parallelepiped having the column vectory of the square matrix as its sides. The in case of rectuonglucy matrix ( 2x3), it dogt make sense to define the determinant bez there are three 2-dim vectors which don't form a parallelogrom when drawn from the origin in a Cartesion cardinute systen. 6 Upper traianglun Madrix on to a b c o de о с.

let 1 2 3 o 5 6 = 1 (584 - 0X6) +2loxsa axa I AI Io 04 +3(oxo-oxs, (A) = 1 (200) +2(0-0) +3 (oro) T14) = 20 2x 2 madrian b a A = 1 Ted 222 2- Row 2 Column 1 3 4 1 Al- 326-5X4 15 6 IAI = 18-20 T1A) = -2