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Chapter 6: Q43E (page 309)

For every nonzero2脳2 matrix A there exists a 2脳2 matrix B such that det(A+B)鈮�detA+detB.

Short Answer

Expert verified

Therefore, det(A+B)鈮�detA+detB. So, the given statement is true.

Step by step solution

01

Matrix Definition

Matrix is a set of numbers arranged inrowsandcolumnsso as to form a rectangulararray.

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�m by n鈥� matrix, written 鈥�m脳n .鈥�

02

To check whether the given condition is true or false

For any invertible matrixA, we can choose

B=0000

Indeed,

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

Therefore,

det(A+B)鈮�detA+detB.

So, the given statement is true.

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