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Chapter 8: Q14E (page 413)

The determinant of a negative definite4脳4matrix must be positive.

Short Answer

Expert verified

The given statement is TRUE.

Step by step solution

01

Check whether the given statement is TRUE or FALSE

The Eigen values of a negative definite matrix are negative.

Hence any 4脳4negative definite matrices will have 4 negatives (may not be distinct) Eigenvalues.

It is know that the determinant is the product of the Eigenvalues of the matrix and the product of 4 negative numbers is positive, so, the determinant of a negative definite 4脳4matrix is positive.

02

Final Answer

The given statement is TRUE.

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