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Chapter 6: Q31E (page 309)

There exist real invertible 3脳3 matrices A andSsuch thatS-1AS=2A .

Short Answer

Expert verified

Therefore, the given statement is not satisfied.

Step by step solution

01

Matrix Definition

Matrix is a set of numbers arranged in rows and columns so as to form a rectangular array.

The numbers are called the elements, or entries, of the matrix.

If there are m rows and n columns, the matrix is said to be an 鈥渕 by n鈥� matrix, written 鈥�m脳n .鈥�

02

To check whether the given condition is true or false

We know that determinant of similar matrices is equal.

So, det(A) must be equal to det(2A) which is false.

The question is whether there exists an invertible 3脳3matrix A such that A and 2A are similar.

If they were similar, it would have to apply

detA = det2A

det A = 8det A.

Which, since detA鈮�0, is a contradiction. Therefore, the given statement is not satisfied.

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Find the determinants of the linear transformations in Exercises 17 through 28.

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