Qanday shartlarda ?
a) agar A matrisa tartibi 4 ga teng bo`lsa b) agar A matrisa tartibi 2 ga teng bo`lsa
v) har qanday bo`lganda ham g) tenglik bajarilmaydi d) agar A matrisa diagonal matrisa bo`lsa
Agar n – tartibli matrisani 1 – chi ustun elementlarini oxirgi o`ringa almashtirsak, qolganlarini chapga o`rinlarini o`zgartirmasdan siljitsak, shu n – tartibli matrisaning determinanti qanday o`zgaradi.
a) agar n – juft bo`lsa, determinant ishorasi qarama – qarshisiga almashadi, agar n –
toq bo`lsa, determinant ishorasi o`zgarmaydi. b) determinant o`zgarmaydi
v) determinant ishorasi qarama – qarshisiga almashadi
g) agar agar n – juft bo`lsa, determinant o`zgarmaydi, n – toq bo`lsa, determinant
ishorasi qarama – qarshisiga o`zgaradi. d) determinant 0 ga teng bo`ladi
Qanday almashtirishlarda matrisa determinanti o`zgarmaydi.
1) transponerlaganda
2) matrisani ihtiyoriy 2 ta satri elementlari almashtirilganda
3) matrisani biror satr elementlarini noldan farqli biror songa ko`paytirganda
4) agar matrisa biror satr elementlarini noldan farqli qandaydir songa ko`paytirib boshqa satr mos elementlariga qo`shsak
a) 1), 2), 3), 4) b) 1), 3) v) 2), 3) g) 1), 4) d) 1), 2), 4)
Matrisa determinanti qanday shartlarda nolga teng bo`ladi.
1) agar matrisa diagonal ko`rinishda bo`lsa
2) agar matrisa nol satrga ega bo`lsa
3) agar matrisa ikkita bir hil ustunga ega bo`lsa
4) agar matrisa nol matrisa bo`lsa
5) agar matrisa 2 ta proporsional satrga ega bo`lsa
a) 1), 2), 3) b) 1), 2), 4) v) 1), 2), 3), 4) g) 2), 3), 4), 5) d) 1), 4), 5)
A kvadrat matrisa uchun quyidagilardan qaysi biri teng kuchli.
1)
2) matrisa satr yoki ustunlari chiziqli bog`liqmas bo`lsa
3) A matrisa teskarilanuvchan
4) A matrisa uchburchak ko`rinishida bo`lsa
a) 1), 2), 3) b) bu yuqoridagilar hammasi teng kuchli v) 1), 3), 4)
g) 1), 4) d) 2), 3), 4)
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