   Chapter 11.3, Problem 58E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# SKILLS Plus 5 7 − 6 0 . When do matrices have inverses Find the inverse of the matrix. For what value(s) of x , if any, does the matrix have no inverse? [ e x − e 2 x e 2 x e 3 x ]

To determine

To find:

The inverse of the given matrix [exe2xe2xe3x] and the value(s) of x the such that inverse of [exe2xe2xe3x] does not exist.

Explanation

Approach:

If a 2×2 matrix A=[abcd], then

If adbc=0, then the inverse does not exist.

Calculation:

Consider A=[exe2xe2xe3x]

Thus,

Now, 2e4x0 for any real value of x, hence inverse of [exe2xe2xe3x] exists for all real values of x and is given by:

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