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Math / Linear Algebra and Its Applications, 4 / Chapter 6 / Problem 6.2.1

Linear Algebra and Its Applications, | 4th Edition | ISBN: 9780030105678 | Authors: Gilbert Strang

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For what range of numbers a and b are the matrices A and B positive definite? A = a 2 2

Chapter 6, Problem 6.2.1

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QUESTION:

For what range of numbers a and b are the matrices A and B positive definite? A = a 2 2 2 a 2 2 2 a B = 1 2 4 2 b 8 4 8 7

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QUESTION:

For what range of numbers a and b are the matrices A and B positive definite? A = a 2 2 2 a 2 2 2 a B = 1 2 4 2 b 8 4 8 7

ANSWER:

Step 1 of 3

Use determinant test, to find the range of numbers for matrix is positive definite.

Recall the determinant test in which all the upper left submatrices where of matrix have positive determinant.

Solve for and its determinant is as follows:

Solve for and its determinant is as follows:

Thus, the values of are .

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