Refer to the vector space axioms given in class. Determine whether each statement is trueor false. If true, explain why, and if false, give a specific example.The set of complex numbers is closed under multiplication.b. The set of 2 x 2 singular matrices is a vector space.The set of all continuous functions fon [0,2] such that f(1) 0 is a vector space.1.a.с.

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Asked Sep 15, 2019
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Refer to the vector space axioms given in class. Determine whether each statement is true
or false. If true, explain why, and if false, give a specific example.
The set of complex numbers is closed under multiplication.
b. The set of 2 x 2 singular matrices is a vector space.
The set of all continuous functions fon [0,2] such that f(1) 0 is a vector space.
1.
a.
с.
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Refer to the vector space axioms given in class. Determine whether each statement is true or false. If true, explain why, and if false, give a specific example. The set of complex numbers is closed under multiplication. b. The set of 2 x 2 singular matrices is a vector space. The set of all continuous functions fon [0,2] such that f(1) 0 is a vector space. 1. a. с.

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Expert Answer

Step 1

To find the truth or falsity of the given statements

Step 2

a) LTRUE: the product of any two complex numbers a+ib and c+id is again a complex number.

a)TRUE:Let,a.b.c.de R.Then
(a+ib)lc+id)=(ac-bd)+i(a +be)
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a)TRUE:Let,a.b.c.de R.Then (a+ib)lc+id)=(ac-bd)+i(a +be)

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Step 3

b)FALSE: By definition, a square matrix is singular if its determinant is 0. The example shown proves th...

b)FALSE: The matrices
1 0
0 0
are both sin gular
A
,В.
0 0
0 1
1 0
is not sin gular
0 1
but A+ B
det(A) det(B) 0,but det(A+ B) 1
So, A,B sin gular,but A+B is not
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b)FALSE: The matrices 1 0 0 0 are both sin gular A ,В. 0 0 0 1 1 0 is not sin gular 0 1 but A+ B det(A) det(B) 0,but det(A+ B) 1 So, A,B sin gular,but A+B is not

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