Determine whether the set, together with the indicated operations, is a vector s

Question

Determine whether the set, together with the indicated operations, is a vector space. If it is not, then identify one of the vector space axioms that fails. The set of all 3 times 3 matrices of the form [a 0 b c 0 0 d e f] with the standard operations The set is a vector space. The set is not a vector space because it is not closed under addition. The set is not a vector space because an additive identity does not exist. The set is not a vector space because an additive inverse does not exist. The set is not a vector space because it is not closed under scalar multiplication.

Explanation / Answer

Here option 5 is correct since for closed under multiplication

c A € V (VECTOR SPACE)

But after multiplication determinant does not belong to same sub space hence this is not the vector space.

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