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(Solved): Show all your work. No points will be given to correct answers without reasonable work. Please write ...



Show all your work. No points will be given to correct answers without reasonable work. Please write your Ankara Science University Student ID number:

N=

the sum of integers in the empty boxes. If you do not write the

N

obtained from your ID number, you will get zero. Show all your work. No points will be given to correct answers without reasonable work. Q1) (A) pts.) Determine whether the statement is True or False. Justify your answer using mathematical arguments( counterexamples, known theorems, or proofs). (a) If

A=[[4,-3,N],[2,N+1,0],[1,-1,1]]

, then

A

is not diagonalizable. (b) If

A

and

B

are nonzero

2\times 2

matrices, then

(A+B)^(2)=A^(2)+2AB+B^(2)

. Determine whether the statement is True or False. Justify your answer using mathematical arguments( counterexamples, known theorems, or proofs) (c) Let

P_(2)

be the vector space of all polynomials of degree 2 or less and the zero polynomial. Then

B={4x^(2)+3x+2,2x^(2)+x,x^(2)+x+1}

form a basis for

P_(2)

.

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