MTH1230 Linear Algebra -- Exam 4 -- Solutions

Problem 1

v1={-4,-2};v2={2,-1};v3={3,2};v4={-1,4};

Abs[Det[{v2-v1,v3-v1}]]/2+Abs[Det[{v4-v1,v3-v1}]]/2

A={{2,0},{2,1},{1,1},{3,1}};

Sqrt[Det[Transpose[A].A]]

Problem 3

S={{2,4},{-3,-5}}

d={{-7,0},{0,3}}

Inverse[S]

A=S.d.Inverse[S]

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Problem 5

A={{-2,0,0},{0,4,-3},{0,1,8}}

Eigenvalues[A]

S=Transpose[Eigenvectors[A]]

d=DiagonalMatrix[Eigenvalues[A]]

A==S.d.Inverse[S]