Complexity Explorer Santa Fe Institute

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Vector and Matrix Algebra

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2.5 Determinants » Quiz #13 Solution

Question 1: det \begin{bmatrix} \ -1& 2 ___ \\ 4 & -4 \end{bmatrix} = (-1)(-4)-(2)(4)=-4.

 

Question 2: A is invertible because its determinant (-4)  is nonzero. 

 

Question 3:  det \begin{bmatrix} \ 1& 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \\ \end{bmatrix} = (1) [(5)(9)- (6)(8)] - (2) [(4)(9)- (6)(7)] +(3) [(4)(8)- (5)(7)] = 0

 

Question 4:  det(B) =0 so B is not invertible.