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Math / Linear Algebra and Its Applications, 4 / Chapter 4 / Problem 4.3.12

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

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Suppose the matrix A is fixed, except that a11 varies from to +. Give examples in which

Chapter 4, Problem 4.3.12

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QUESTION:

Suppose the matrix A is fixed, except that a11 varies from to +. Give examples in which detA is always zero or never zero. Then show from the cofactor expansion (8) that otherwise detA = 0 for exactly one value of a11.

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QUESTION:

Suppose the matrix A is fixed, except that a11 varies from to +. Give examples in which detA is always zero or never zero. Then show from the cofactor expansion (8) that otherwise detA = 0 for exactly one value of a11.

ANSWER:

Step 1 of 3

Let be an fixed matrix with an exception of the element .

As per the cofactor expansion formula,

Assuming the determinant value of matrix as zero,

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