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Chapter 2: Q30E (page 98)

For which values of the constants b and c is the following matrix invertible?

[01b-10-c-b-c0]

Short Answer

Expert verified

The matrix[01b-10-c-b-c0] is not invertible for any value of b and c.

Step by step solution

01

  Definition of an invertible matrix

A matrix A of order n x n is called an invertible matrix if (and only if) the determinant of matrix A is equal to zero.

i.e. A=0

02

  Finding the determinant of the given matrix

LetA=[01b-10-c-b-c0]

Find the determinant as:

A=00-c-10-bc+bc-0A=0+bc-bcA=0

Since the determinant of the matrix A is equal to zero. Therefore, the matrix A is not invertible for any value of b and c.

03

  Final Answer

The matrix[01b-10-c-b-c0] is not invertible for any value of b and c.

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