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Chapter 2: Q37E (page 108)

If matrix A is invertible, then matrix 5A must be invertible as well.

Short Answer

Expert verified

The statement is true.

Step by step solution

01

Explaining

The claim is that if A is invertible then so is 5A. To check this we will find5A-1 if it exists:

5A-1=5-1A-1=15A-1

02

Result

Since we know that A is invertible we know that5A-1 is defined and the statement is true.

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Most popular questions from this chapter

Matrixis invertible for all real numbers k.

Consider the circular face in the accompanying figure. For each of the matrices A in Exercises 24 through 30, draw a sketch showing the effect of the linear transformationT(x)鈫�=Ax鈫�on this face.

28.[1002]

Write all possible forms of elementary2脳2E5=10k1matrices E. In each case, describe the transformationy鈫�=Ex鈫�geometrically.

The formula AB=BAholds for alln脳n matrices A and B .

Question: Consider the matrix A2 in Example 4 of Section 2.3.

  1. The third component of the first column ofA2 is 1/4 . What does this entry mean in practical terms, that is, in terms of surfers following links in our mini-Web?
  2. When is the i j thentry of A2 equal to 0 ? Give your answer both in terms of paths of length 2 in the graph of the mini-Web and also in terms of surfers being able to get from page j to pageiby following two consecutive links.
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