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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

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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.

Therefore, det(A+B)det A+det B. So, the given statement is true.

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

For any invertible matrix A , we can choose



det( A+B)=det Adet( A+B)=detA+0


det( A+B)det A+det B .

So, the given statement is true.

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