• :00Days
  • :00Hours
  • :00Mins
  • 00Seconds
A new era for learning is coming soonSign up for free
Log In Start studying!

Select your language

Suggested languages for you:
Answers without the blur. Sign up and see all textbooks for free! Illustration

Q32 E

Linear Algebra With Applications
Found in: Page 309
Linear Algebra With Applications

Linear Algebra With Applications

Book edition 5th
Author(s) Otto Bretscher
Pages 442 pages
ISBN 9780321796974

Answers without the blur.

Just sign up for free and you're in.


Short Answer

There exist real invertible 3×3 matrices A and S such that .

Therefore, the given statement is not satisfied.

See the step by step solution

Step by Step Solution

Step 1: 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 “m by n” matrix, written “m×n .”

Step 2: To check whether the given condition is true or false

On taking determinant


Which is false, as det(S) turns out to be imaginary.

The question is whether there exists an invertible 3×3 matrix A such that A and 2A are similar. If they were similar, it would have to apply

det A = det(-A)

det A = - detA,

Which, since detA0, is a contradiction. Therefore, the given statement is not satisfied.

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free
94% of StudySmarter users get better grades.