In each of the following assume the usual definition of vectoraddition and scala

Question

In each of the following assume the usual definition of vectoraddition and scalar multiplication is used, unless otherwisespecified.

From the following select the one(s) that are vector spaces. A The set of all 3 × 3 matrices of theform
é
ê
ê
ê
ë 0 0 0 0 0 a c b 0 ù
ú
ú
ú
û where a, b, c ÎR. B The set of all 2 × 2 matrices of theform
é
ê
ê
ë a 2 2 b ù
ú
ú
û where a, b ÎR. C
W = ì
ï
í
ï
î é
ê
ê
ë x1 x2 ù
ú
ú
û : x1 x2³ 0 ü
ï
ý
ï
þ D The set of all polynomials with constant termequal to zero. None of the above A The set of all 3 × 3 matrices of theform
é
ê
ê
ê
ë 0 0 0 0 0 a c b 0 ù
ú
ú
ú
û where a, b, c ÎR. B The set of all 2 × 2 matrices of theform
é
ê
ê
ë a 2 2 b ù
ú
ú
û where a, b ÎR. C
W = ì
ï
í
ï
î é
ê
ê
ë x1 x2 ù
ú
ú
û : x1 x2³ 0 ü
ï
ý
ï
þ D The set of all polynomials with constant termequal to zero. None of the above

Explanation / Answer

answer is A.

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