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Chapter 4: Q24. (page 199)

Find the inverse of each matrix, if it exists.24.

[−3−264]

Short Answer

Expert verified

The inverse of the matrix 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 A be the matrix [−3−264]

That is,A=[−3−264]

Comparing with the standard form A=[abcd], a=−3,b=−2,c=6,d=4.

Then, A−1 is:A−1=1ad−bc[d−b−ca]=1(4×−3)−(−2×6)[4−(−2)−6−3]=1−12+12[42−6−3]

Here,

ad−bc=−12+12=0

As ad−bc=0 here, inverse does not exist.

03

- State the conclusion.

Therefore, the inverse of the matrix [−3−264] does not exist.

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