Multiple Choice
Let ,
,
be m-forms,
be a k-form, and
be an l-form on
. Which of the following properties of the wedge product is not always true?
A) ( +
)
11ee7bbb_54a1_6c9e_ae82_5397d9492c20_TB9661_11 = 11ee77e1_778e_5ec4_a0f8_3957ae8e208f_TB9661_11 11ee7bbb_c9fe_971f_ae82_3b4fcccd2417_TB9661_11 11ee7bbb_54a1_6c9e_ae82_5397d9492c20_TB9661_11 + 11ee77e1_778e_5ec5_a0f8_914525eec565_TB9661_11 11ee7bbb_c9fe_971f_ae82_3b4fcccd2417_TB9661_11 11ee7bbb_54a1_6c9e_ae82_5397d9492c20_TB9661_11
B) (11ee7bbc_2f42_a9a0_ae82_03df16557ec6_TB9661_11 11ee7bbb_c9fe_971f_ae82_3b4fcccd2417_TB9661_11 11ee7bbb_54a1_6c9e_ae82_5397d9492c20_TB9661_11 ) 11ee7bbb_c9fe_971f_ae82_3b4fcccd2417_TB9661_11 11ee7bbc_854e_b551_ae82_a1ccb48ff30b_TB9661_11 = 11ee7bbc_2f42_a9a0_ae82_03df16557ec6_TB9661_11 (11ee7bbb_54a1_6c9e_ae82_5397d9492c20_TB9661_1111ee7bbb_c9fe_971f_ae82_3b4fcccd2417_TB9661_11 11ee7bbc_854e_b551_ae82_a1ccb48ff30b_TB9661_11 )
C) 11ee7bbc_2f42_a9a0_ae82_03df16557ec6_TB9661_11 11ee7bbb_c9fe_971f_ae82_3b4fcccd2417_TB9661_11 11ee7bbb_54a1_6c9e_ae82_5397d9492c20_TB9661_11 = - 11ee7bbb_54a1_6c9e_ae82_5397d9492c20_TB9661_11 11ee7bbb_c9fe_971f_ae82_3b4fcccd2417_TB9661_11 11ee7bbc_2f42_a9a0_ae82_03df16557ec6_TB9661_11
D) (a 11ee7bbc_2f42_a9a0_ae82_03df16557ec6_TB9661_11 ) 11ee7bbb_c9fe_971f_ae82_3b4fcccd2417_TB9661_11 11ee7bbb_54a1_6c9e_ae82_5397d9492c20_TB9661_11 = a (11ee7bbc_2f42_a9a0_ae82_03df16557ec6_TB9661_1111ee7bbb_c9fe_971f_ae82_3b4fcccd2417_TB9661_11 11ee7bbb_54a1_6c9e_ae82_5397d9492c20_TB9661_11 ) for a 11ee7b17_3372_5854_ae82_d19d2ea0c252_TB9661_11 R
E) for every k 1, there exists a zero k-form such that 11ee7bbb_54a1_6c9e_ae82_5397d9492c20_TB9661_11 + 0 = 11ee7bbb_54a1_6c9e_ae82_5397d9492c20_TB9661_11, and 0 11ee7bbb_c9fe_971f_ae82_3b4fcccd2417_TB9661_11 11ee7bbc_854e_b551_ae82_a1ccb48ff30b_TB9661_11 = 0.
Correct Answer:

Verified
Correct Answer:
Verified
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