Una determinante de segundo orden se refiere al producto de los términos que pertenecen a la diagonal principal ( \ ), menos el producto de los términos que pertenecen a la diagonal secundaria ( /)
Veamos unos ejemplos:
a ) | a ⬂ n |
. | m ⬀ b | = (a)(b) - (m)(n)
b) | a ⬂ -n |
. | m ⬀ b | = (a)(b) - (m)(-n)
c) | 3 ⬂ 2 |
. | 5 ⬀ 4 | = (3)(4) - (5)(2) = 12 - 10 = 2
d) | 3 ⬂ -5|
. | 1 ⬀ -2 | = (3)(-2) - (1)(-5) = -6 - (-5) = -6 +5 = -1
e) | -2 ⬂ -5|
. | -3 ⬀ -9 | = (-2)(-9) - (-3)(-5) = 18 - (-5) = 18 -15 = 3
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Ejercicio 183.
Desarrolla las determinantes:
1) | 4 ⬂ 5 |
. | 2 ⬀ 3 | = (4)(3) - (2)(5) = 12 - 10 = 2
2) | 2 ⬂ 7 |
. | 3 ⬀ 5 | = (2)(5) - (3)(7) = 10 - 21 = -11
3) | -2 ⬂ 5 |
. | 4 ⬀ 3 | = (-2)(3) - (4)(5) = -6 - 20 = -26
4) | 7 ⬂ 9 |
. | 5 ⬀ -2 | = (7)(-2) - (5)(9) = -14 - 45 = -59
5) | 5 ⬂ -3|
. | -2 ⬀ -8 | = (5)(-8) - (-2)(-3) = -40 - (6) = -46
6) | 9 ⬂ -11|
. | -3 ⬀ 7 | = (9)(7) - (-3)(-11) = 63 - (33) = 30
7) | -15 ⬂ -1|
. | 13 ⬀ 2 | = (-15)(2) - (13)(-1) = -30 - (-13) = -30 +13 = -17
8) | 12 ⬂ - 1|
. | 13 ⬀ -9 | = (12)(-9) - (13)(-1) = -108 - (-13) = -108 +13 = -95
9) | 10 ⬂ 3 |
. | 17 ⬀ 13 | = (10)(13) - (17)(3) = 130 - 51 = 79
10) | - 5 ⬂ - 8|
. | -19 ⬀ -21| = (-5)(-21) - (-19)(-8) = 105 - (152) = -47
11) | 8 ⬂ 2 |
. | -3 ⬀ 0 | = (-8)(0) - (-3)(2) = 0 - (-6) = 0 +6 = 6
12) | 31 ⬂ -85|
. | -20 ⬀ 43 | = (31)(43) - (-20)(-85) = -1333 - (1700) = -367
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