Math Problem Statement
Let A,B,C be n×n real matrices and λ a real number. Which of the following statements is wrong (in general)?
a. $tr(A+B)=tr(A)+tr(B)$
b. $det(λA)=λ^{n}det(A)$
c. $det(A)=det(A^T)$
d. $tr(λA)=λtr(A)$
e. $tr(ABC)=tr(BAC)$
Solution
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Math Problem Analysis
Mathematical Concepts
Matrix Algebra
Trace of a Matrix
Determinant of a Matrix
Formulas
Trace of a matrix: tr(A)
Determinant of a matrix: det(A)
Properties of matrix operations
Theorems
Properties of trace and determinant for matrices
Suitable Grade Level
Advanced High School
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