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Chapter 4: Q28. (page 199)

Find the inverse of each matrix, if it exists.28.

[−466−9]

Short Answer

Expert verified

The inverse of the matrix is does not exist.

Step by step solution

01

- Define inverse of a matrix.

For the matrix A ,

A=[abcd]

The inverse of matrix of the matrix A is:

A−1=1ad−bc[d−b−ca]

where ad−bc≠0. ad−bc is the determinant of the matrix A .

If ad−bc=0, the inverse of a matrix doesn not exist.

02

- Calculate the inverse.

Let be the matrix[−466−9]

That is,A=[−466−9]

Comparing with the standard form A=[abcd], a=−4,b=6,c=6,d=−9.

Then, A−1 is:

A−1=1ad−bc[d−b−ca]=1(−4×−9)−(6×6)[−9−6−6−4]=136−36[−9−6−6−4]

Here, ad−bc=36−36=0

And inverse exist only if ad−bc≠0.

As ad−bc=0 here, inverse doesnot exist.

03

- State the conclusion.

Therefore, the inverse of the matrix [−466−9] does not exist.

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