Determinants

Square Matrix
A matrix whose number of rows and columns are equal.  
A square matrix can also be called a matrix of the nth order(n being the size of the matrix)

Square Matrix of 3rd order

Every square matrix A has a determinant, |A|.  The method of finding the determinant depends on the size of the matrix.

Determinant of 2^nd Order Matrix

Given

the determinant is |A| = ad - cb

To give a more graphical look at this process examine the following

Thus, |A| = (red product) - (blue product)

Numerical example of 2x2 Determinant

Given B, find |B|.

|B| = (1)(5) - (4)(-2)
|B| = 5 + 8
|B| = 13

2nd Order Determinant Practice: Given the 2 x 2 matrices, find each of the following determinants.

#1) Find |C|

#2) Find |D|

Determinant of 3^rd Order Matrix

Given

|A| = a(ei-hf) - b(di - gf) + c(dh - ge)

 To give a more graphical look at this process examine the following

This can also be thought of as 

Numerical example of 3x3 Determinant

Given B, find |B|.

|B| = 1[(-2)(8) - (10)(7)] - 4[(3)(8) - (0)(7)] + -5[(3)(10) - (0)(-2)]
|B| = 1[-16 - 70] - 4 [24 - 0] + -5[30 - 0]
|B| = 1[-86] - 4[24] + -5[30]
|B| = -86 - 96 - 150
|B| = -332

3rd Order Determinant Practice: Given the 3 x 3 matrices, find each of the following determinants.

#1) Find |C|

#2) Find |D|

Homework

Determinants

Given the matrices, find each calculation.

#1) |A|
#2) |B|
#3) |C|
#4) |D|
#5) |E|
#6) |F|
#7) |G|
#8) |H|
#9) 5|A|
#10) -|D| + 9|E|
#11) 10|H| + 5|G| - 2|E|

Answers

#1) |A| = 7
#2) |B| = -8
#3) |C| = 5
#4) |D| = 80
#5) |E| = -11
#6) |F| = 11
#7) |G| = -17
#8) |H| = -10
#9) 5|A| = 35
#10) -|D| = -179
#11) 10|H| + 5|G| - 2|E| = -163