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

For every nonzero $2 \times 2$ matrix A there exists a $2 \times 2$ matrix B such that $d e t (A + B) \neq d e t A + d e t B$ .

Therefore, $d e t (A + B) \neq d e t A + d e t B .$ So, the given statement is true.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

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 “ $m \times n$ .”

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

For any invertible matrix A , we can choose

$B = [\begin{matrix} 0 & 0 \\ 0 & 0 \end{matrix}]$

Indeed,

$d e t (A + B) = d e t A d e t (A + B) = d e t A + 0$

Therefore,

$d e t (A + B) \neq d e t A + d e t B$ .

So, the given statement is true.

Find Study Materials for

Create Study Materials

Select your language

Linear Algebra With Applications

Answers without the blur.

Short Answer

For every nonzero $2 \times 2$ matrix A there exists a $2 \times 2$ matrix B such that $d e t (A + B) \neq d e t A + d e t B$ .

Step by Step Solution

Step 1: Matrix Definition

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

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Select your language

Linear Algebra With Applications

Answers without the blur.

Short Answer

For every nonzero 2×2 matrix A there exists a 2×2 matrix B such that det(A+B)≠det A+det B.

Step by Step Solution

Step 1: Matrix Definition

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

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Probability and Statistics

Statistics

Mechanics Maths

Geometry

Pure Maths

For every nonzero $2 \times 2$ matrix A there exists a $2 \times 2$ matrix B such that $d e t (A + B) \neq d e t A + d e t B$ .